A318624 - OEIS

%I #16 Mar 27 2019 12:18:38

%S 0,1,10,30,55,91,138,190,253,327,406,496,597,703,820,948,1081,1225,

%T 1380,1540,1711,1893,2080,2278,2487,2701,2926,3162,3403,3655,3918,

%U 4186,4465,4755,5050,5356,5673,5995,6328,6672,7021,7381,7752,8128,8515,8913,9316

%N Number of 3-member subsets of [3*n] whose elements sum to a multiple of n.

%H Alois P. Heinz, <a href="/A318624/b318624.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).

%F G.f.: -x*(3*x^4+4*x^3+11*x^2+8*x+1)/((x^2+x+1)*(x-1)^3).

%F a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-4) +a(n-5) for n>5.

%F 3*a(n) = 5+2*A099837(n)+27*n*(n-1)/2 for n>0. - _R. J. Mathar_, Sep 02 2018

%e a(1) = 1: {1,2,3}.

%e a(2) = 10: {1,2,3}, {1,2,5}, {1,3,4}, {1,3,6}, {1,4,5}, {1,5,6}, {2,3,5}, {2,4,6}, {3,4,5}, {3,5,6}.

%e a(3) = 30: {1,2,3}, {1,2,6}, {1,2,9}, {1,3,5}, {1,3,8}, {1,4,7}, {1,5,6}, {1,5,9}, {1,6,8}, {1,8,9}, {2,3,4}, {2,3,7}, {2,4,6}, {2,4,9}, {2,5,8}, {2,6,7}, {2,7,9}, {3,4,5}, {3,4,8}, {3,5,7}, {3,6,9}, {3,7,8}, {4,5,6}, {4,5,9}, {4,6,8}, {4,8,9}, {5,6,7}, {5,7,9}, {6,7,8}, {7,8,9}.

%t LinearRecurrence[{2,-1,1,-2,1},{0,1,10,30,55,91},50] (* _Harvey P. Dale_, Mar 27 2019 *)

%Y Row n=3 of A318557.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Aug 30 2018