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 A381291 #22 Feb 28 2025 07:45:41 %S A381291 1,5,15,43,99,217,429,809,1430,2438,3978,6310,9690,14550,21318,30666, %T A381291 43263,60115,82225,111041,148005,195143,254475,328755,420732,534076, %U A381291 672452,840652,1043460,1287036,1577532,1922740,2330445,2810385,3372291,4028183,4790071 %N A381291 Number of subsets of 8 integers between 1 and n such that their sum is 0 modulo n. %C A381291 For an integer s multiple of 8, this is also the number of subsets of 8 integers between 1 and n such that their sum is s modulo n. %H A381291 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 A381291 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-4,11,-8,0,8,-10,0,8,0,-10,8,0,-8,11,-4,-4,4,-1). %F A381291 G.f.: x^9*(1 + x - x^2 + 7*x^3 - 4*x^4 + 6*x^5 + 4*x^6 - 4*x^7 + 3*x^8 + 5*x^9 - 3*x^10 + x^11)/((1 - x)^4*(1 - x^2)^2*(1 - x^4)*(1 - x^8)). %e A381291 For n=10, there are a(10)=5 order 8 subsets of Z/10Z with sum equal to 0 mod 10. %Y A381291 Cf. A381290, A381289, A011796. %K A381291 nonn %O A381291 9,2 %A A381291 _Xavier Roulleau_ and _David Broadhurst_, Feb 19 2025