A318624 Number of 3-member subsets of [3*n] whose elements sum to a multiple of n.

0, 1, 10, 30, 55, 91, 138, 190, 253, 327, 406, 496, 597, 703, 820, 948, 1081, 1225, 1380, 1540, 1711, 1893, 2080, 2278, 2487, 2701, 2926, 3162, 3403, 3655, 3918, 4186, 4465, 4755, 5050, 5356, 5673, 5995, 6328, 6672, 7021, 7381, 7752, 8128, 8515, 8913, 9316

Offset: 0

Author

Alois P. Heinz, Aug 30 2018

Keywords

• nonn
• easy

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).

Crossrefs

Row n=3 of A318557.

Programs

Mathematica

LinearRecurrence[{2,-1,1,-2,1},{0,1,10,30,55,91},50] (* Harvey P. Dale, Mar 27 2019 *)

Formula

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

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

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