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 A381290 #22 Feb 28 2025 07:45:46
%S A381290 1,4,9,22,42,78,132,217,333,504,728,1035,1428,1944,2583,3399,4389,
%T A381290 5616,7084,8866,10962,13468,16380,19806,23751,28336,33561,39576,46376,
%U A381290 54126,62832,72675,83655,95988,109668,124929,141778,160468,180999
%N A381290 Number of subsets of 6 integers between 1 and n such that their sum is 1 modulo n.
%C A381290 For s an integer such that GCD(s,6)=1, this is also the number of subsets of 6 integers between 1 and n such that their sum is s modulo n.
%H A381290 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 A381290 <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 A381290 G.f.: x^7*(1 + 2*x + 3*x^3 + 2*x^4 + 2*x^5 + x^6 + x^7)/((1 - x)^2*(1 - x^2)^2*(1 - x^3)*(1 - x^6)).
%e A381290 For n=7, a(7)=1 since the set {0,1,2,3,4,5} is the unique order 6 subset of Z/7Z with sum equal to 1 mod 7.
%Y A381290 Cf. A381289, A011796.
%K A381290 nonn,easy
%O A381290 7,2
%A A381290 _Xavier Roulleau_ and _David Broadhurst_, Feb 19 2025