A275874 a(n) = (n-4)*(n+1)*(n+3)/6.

0, 8, 21, 40, 66, 100, 143, 196, 260, 336, 425, 528, 646, 780, 931, 1100, 1288, 1496, 1725, 1976, 2250, 2548, 2871, 3220, 3596, 4000, 4433, 4896, 5390, 5916, 6475, 7068, 7696, 8360, 9061, 9800, 10578, 11396, 12255, 13156, 14100, 15088, 16121, 17200, 18326, 19500, 20723, 21996

Offset: 4

Author

N. J. A. Sloane, Aug 14 2016

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 4..1000
• Hilton, Peter John, and Jean Pedersen, Descartes, Euler, Poincaré, Pólya and Polyhedra, L'Enseign. Math., 27 (1981), 327-343. See Cor. 1.
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

A137742 is an essentially identical sequence.

Programs

Maple

a := n -> (n - 4)*(n + 1)*(n + 3)/6:
seq(a(n), n = 4..51); # Peter Luschny, Jan 25 2019

PARI

concat(0, Vec(x^5*(8-11*x+4*x^2)/(1-x)^4 + O(x^50))) \\ Colin Barker, Aug 15 2016

Formula

From Colin Barker, Aug 15 2016: (Start)

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 7.

G.f.: x^5*(8 - 11*x + 4*x^2) / (1 - x)^4.

(End)