This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A381289 #35 Feb 28 2025 07:45:37 %S A381289 1,3,10,20,42,76,132,212,335,497,728,1028,1428,1932,2586,3384,4389, %T A381289 5601,7084,8844,10966,13442,16380,19780,23751,28301,33566,39536,46376, %U A381289 54086,62832,72624,83661,95931,109668,124872,141778,160398,181006 %N A381289 Number of subsets of 6 integers between 1 and n such that their sum is 0 modulo n. %C A381289 For an integer s multiple of 6, this is also the number of subsets of 6 integers between 1 and n such that their sum is s modulo n. %H A381289 David Broadhurst and Xavier Roulleau, <a href="https://arxiv.org/abs/2502.19523">Number of partitions of modular integers</a>, arXiv:2502.19523 [math.NT], 2025. %H A381289 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-3,-1,1,4,-3,-3,4,1,-1,-3,1,2,-1). %F A381289 G.f.: x^7*(1 + x + 3*x^2 + 2*x^4 + 4*x^5 + x^6 - x^7 + x^8)/((1 - x)^2*(1 - x^2)^2*(1 - x^3)*(1 - x^6)). - _David Broadhurst_, Feb 19 2025 %e A381289 For n=8, there are a(8)=3 order 6 subsets of Z/8Z with sum equal to 0 mod 8. %Y A381289 Cf. A011796. %K A381289 nonn,easy %O A381289 7,2 %A A381289 _Xavier Roulleau_ and _David Broadhurst_, Feb 19 2025