A381291 - OEIS

%I #14 Feb 22 2025 14:54:10

%S 1,5,15,43,99,217,429,809,1430,2438,3978,6310,9690,14550,21318,30666,

%T 43263,60115,82225,111041,148005,195143,254475,328755,420732,534076,

%U 672452,840652,1043460,1287036,1577532,1922740,2330445,2810385,3372291,4028183,4790071

%N Number of subsets of 8 integers between 1 and n such that their sum is 0 modulo n.

%C 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.

%D Sequence studied in: Number of partitions of modular integers, by David Broadhurst and Xavier Roulleau (in preparation).

%F 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 For n=10, there are a(10)=5 order 8 subsets of Z/10Z with sum equal to 0 mod 10.

%Y Cf. A381290, A381289, A011796.

%K nonn,new

%O 9,2

%A _Xavier Roulleau_ and _David Broadhurst_, Feb 19 2025