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%I #16 Feb 23 2025 09:39:10
%S 1,4,9,22,42,78,132,217,333,504,728,1035,1428,1944,2583,3399,4389,
%T 5616,7084,8866,10962,13468,16380,19806,23751,28336,33561,39576,46376,
%U 54126,62832,72675,83655,95988,109668,124929,141778,160468,180999
%N Number of subsets of 6 integers between 1 and n such that their sum is 1 modulo n.
%C 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.
%D Sequence studied in: Number of partitions of modular integers, by David Broadhurst and Xavier Roulleau (in preparation).
%H <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 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 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 Cf. A381289, A011796.
%K nonn,easy,new
%O 7,2
%A _Xavier Roulleau_ and _David Broadhurst_, Feb 19 2025