A204467 Number of 3-element subsets that can be chosen from {1,2,...,6*n+3} having element sum 9*n+6.

1, 8, 25, 50, 85, 128, 181, 242, 313, 392, 481, 578, 685, 800, 925, 1058, 1201, 1352, 1513, 1682, 1861, 2048, 2245, 2450, 2665, 2888, 3121, 3362, 3613, 3872, 4141, 4418, 4705, 5000, 5305, 5618, 5941, 6272, 6613, 6962, 7321, 7688, 8065, 8450, 8845, 9248, 9661

Offset

0,2

Comments

a(n) is the number of partitions of 9*n+6 into 3 distinct parts <= 6*n+3.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2, 0, -2, 1).

Formula

a(n) = 1+floor((3+9/2*n)*n).

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

a(n) = (6*n*(3*n+2)+(-1)^n+3)/4. - Bruno Berselli, Jan 17 2012

a(0)=1, a(1)=8, a(2)=25, a(3)=50, a(n)=2*a(n-1)-2*a(n-3)+a(n-4). - Harvey P. Dale, May 25 2015

Example

a(1) = 8 because there are 8 3-element subsets that can be chosen from {1,2,...,9} having element sum 15: {1,5,9}, {1,6,8}, {2,4,9}, {2,5,8}, {2,6,7}, {3,4,8}, {3,5,7}, {4,5,6}.

Maple

a:= n-> 1 +floor((3+9/2*n)*n):
seq(a(n), n=0..50);

Mathematica

Table[(6n(3n+2)+(-1)^n+3)/4, {n, 0, 50}] (* or *) LinearRecurrence[{2, 0, -2, 1}, {1, 8, 25, 50}, 50] (* Harvey P. Dale, May 25 2015 *)

Crossrefs

Bisection of column k=3 of A204459.

Cf. A104185.

Sequence in context: A089613 A344714 A164754 * A062728 A273982 A244942

Adjacent sequences: A204464 A204465 A204466 * A204468 A204469 A204470

Keyword

nonn,easy

Author

Alois P. Heinz, Jan 16 2012

Status

approved