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 A381351 #15 Feb 28 2025 17:57:25 %S A381351 1,5,19,55,143,335,715,1430,2703,4862,8398,14000,22610,35530,54484, %T A381351 81719,120175,173592,246675,345345,476913,650325,876525,1168710, %U A381351 1542684,2017356,2615103,3362260,4289780,5433736,6835972,8544965,10616489,13114465 %N A381351 Number of subsets of 9 integers between 1 and n such that their sum is 3 modulo n. %C A381351 For s an integer such that GCD(s,9)=3, this is also the number of subsets of 9 integers between 1 and n such that their sum is s modulo n. %H A381351 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 A381351 <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,22,-27,36,-42,36,-27,23,-21,21,-23,27,-36,42,-36,27,-22,15,-6,1). %F A381351 G.f.: x^10*(1 - x + 4*x^2 - 6*x^3 + 15*x^4 - 17*x^5 + 15*x^6 - 6*x^7 + 4*x^8 - x^9 + x^10)/((1 - x)^6*(1 - x^3)^2*(1 - x^9)). %e A381351 For n=10, there are a(10)=1 order 9 subsets of Z/10Z with sum equal to 3 mod 10. %Y A381351 Cf. A011796, A031164, A032194, A381289, A381290, A381291. %K A381351 nonn,easy %O A381351 10,2 %A A381351 _Xavier Roulleau_, Feb 21 2025