cp's OEIS Frontend

A381350 Number of subsets of 8 integers between 1 and n such that their sum is 2 modulo n.

%I A381350 #23 Feb 28 2025 05:59:12
%S A381350 1,5,15,42,99,217,429,808,1430,2438,3978,6308,9690,14550,21318,30664,
%T A381350 43263,60115,82225,111038,148005,195143,254475,328752,420732,534076,
%U A381350 672452,840648,1043460,1287036,1577532,1922736,2330445,2810385,3372291,4028178,4790071,5672645
%N A381350 Number of subsets of 8 integers between 1 and n such that their sum is 2 modulo n.
%C A381350 For s an integer such that GCD(s,8)=2, this is also the number of subsets of 8 integers between 1 and n such that their sum is s modulo n.
%H A381350 Stefano Spezia, <a href="/A381350/b381350.txt">Table of n, a(n) for n = 9..10000</a>
%H A381350 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 A381350 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-4,12,-12,4,12,-22,12,4,-12,12,-4,-4,4,-1).
%F A381350 G.f.: x^9*(1 + x - x^2 + 6*x^3 + 2*x^5 + 6*x^7 - x^8 + x^9 + x^10)/((1 - x)^4*(1 - x^2)^2*(1 - x^4)*(1 - x^8)).
%F A381350 a(n) = (n - 4)*(2520 - 24*(281 + 35*(-1)^n)*n + 5*(1039 + 21*(-1)^n)*n^2 - 2112*n^3 + 452*n^4 - 48*n^5 + 2*n^6 - 2520*A056594(n))/80640. - _Stefano Spezia_, Feb 21 2025
%e A381350 For n=10, there are a(10)=5 order 8 subsets of Z/10Z with sum equal to 2 mod 10.
%Y A381350 Cf. A011796, A031164, A056594, A381289, A381290, A381291.
%K A381350 nonn,easy
%O A381350 9,2
%A A381350 _Xavier Roulleau_, Feb 21 2025