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 A318625 Number of 4-member subsets of [4*n] whose elements sum to a multiple of n. 2

%I #7 Aug 30 2018 22:45:38

%S 0,1,38,165,460,969,1782,2925,4508,6545,9158,12341,16236,20825,26262,

%T 32509,39740,47905,57190,67525,79116,91881,106038,121485,138460,

%U 156849,176902,198485,221868,246905,273878,302621,333436,366145,401062,437989,477260,518665

%N Number of 4-member subsets of [4*n] whose elements sum to a multiple of n.

%H Alois P. Heinz, <a href="/A318625/b318625.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,2,-2,0,2,-1).

%F G.f.: x*(4*x^7+27*x^6+100*x^5+123*x^4+132*x^3+89*x^2+36*x+1) / ((x^2+1) *(x+1)^2 *(x-1)^4).

%e a(2) = 38: {1,2,3,4}, {1,2,3,6}, {1,2,3,8}, {1,2,4,5}, {1,2,4,7}, {1,2,5,6}, {1,2,5,8}, {1,2,6,7}, {1,2,7,8}, {1,3,4,6}, {1,3,4,8}, {1,3,5,7}, {1,3,6,8}, {1,4,5,6}, {1,4,5,8}, {1,4,6,7}, {1,4,7,8}, {1,5,6,8}, {1,6,7,8}, {2,3,4,5}, {2,3,4,7}, {2,3,5,6}, {2,3,5,8}, {2,3,6,7}, {2,3,7,8}, {2,4,5,7}, {2,4,6,8}, {2,5,6,7}, {2,5,7,8}, {3,4,5,6}, {3,4,5,8}, {3,4,6,7}, {3,4,7,8}, {3,5,6,8}, {3,6,7,8}, {4,5,6,7}, {4,5,7,8}, {5,6,7,8}.

%Y Row n=4 of A318557.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Aug 30 2018

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