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

4,2

Links

Colin Barker, Table of n, a(n) for n = 4..1000

Peter John Hilton 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).

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)

From Amiram Eldar, Nov 15 2025: (Start)

Sum_{n>=5} 1/a(n) = 317/1225.

Sum_{n>=5} (-1)^(n+1)/a(n) = 12*log(2)/35 - 177/1225. (End)

Maple

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

Mathematica

a[n_] := (n-4)*(n+1)*(n+3)/6; Array[a, 50, 4] (* Amiram Eldar, Nov 15 2025 *)

Prog

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

Crossrefs

A137742 is an essentially identical sequence.

Sequence in context: A000567 A124484 A137742 * A190456 A188026 A180672

Adjacent sequences: A275871 A275872 A275873 * A275875 A275876 A275877

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 14 2016

Status

approved