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

0,3

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).

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

Example

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}.

Mathematica

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

Crossrefs

Row n=3 of A318557.

Sequence in context: A096844 A031299 A124164 * A255601 A104044 A124080

Adjacent sequences: A318621 A318622 A318623 * A318625 A318626 A318627

Keyword

nonn,easy

Author

Alois P. Heinz, Aug 30 2018

Status

approved