Problem 52729. Easy Sequences 21: Combinatorial Summations

Created by Ramon Villamangca

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<div style = "text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; "><div style="block-size: 205px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-weight: bold; ">Create the function S(n), defined by the following summation</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">:</span></span></div><div style="block-size: 66px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">                               </span></span><img class="imageNode" width="224" height="60" style="vertical-align: baseline;width: 224px;height: 60px" src="data:image/gif;base64,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" data-image-state="image-loaded"></div><div style="block-size: 49px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">The symbol </span></span><img class="imageNode" width="15" height="22" style="vertical-align: baseline;width: 15px;height: 22px" src="data:image/gif;base64,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" data-image-state="image-loaded"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style=""> is the combination function ('nchoosek(a,b)' in MATLAB). 'S(n)' always yields an integer value,  if 'n' is a positive integer. Present the output modulo 1234567.</span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-weight: bold; ">NOTE:</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style=""> S(n) may have positive or negative values. Therefore, please use the 'mod' function instead of the 'rem' function to ensure the result would be a positive modulus.</span></span></div></div></div>

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Last Solution submitted on Jul 17, 2023

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William on 19 Sep 2021

Almost got it, but not quite!

Ramon Villamangca on 19 Sep 2021

Hi William, you are right. The sign should only be negative when n = 2. Thanks.

Rafael S.T. Vieira on 24 Nov 2022

Tip: This problem is not solved using combinations or factorials.

Rafael S.T. Vieira on 24 Nov 2022

S(20) = 177547, you're welcome.

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Problem 52729. Easy Sequences 21: Combinatorial Summations

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Problem 52729. Easy Sequences 21: Combinatorial Summations

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