A272130 a(n) = 16*n^3 + 10*n^2 + 4*n + 1.

1, 31, 177, 535, 1201, 2271, 3841, 6007, 8865, 12511, 17041, 22551, 29137, 36895, 45921, 56311, 68161, 81567, 96625, 113431, 132081, 152671, 175297, 200055, 227041, 256351, 288081, 322327, 359185, 398751, 441121, 486391, 534657, 586015, 640561, 698391

Offset: 0

Author

Vincenzo Librandi, Apr 21 2016

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• M. Beck, J. A. De Loera, M. Develin, J. Pfeifle and R. P. Stanley, Coefficients and roots of Ehrhart Polynomials, Contemp. Math. 374 (2005), 15-36, page 19.
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A144965, A158187, A272039.

Programs

Magma

[16*n^3+10*n^2+4*n+1: n in [0..50]];

Maple

A272130:=n->16*n^3+10*n^2+4*n+1: seq(A272130(n), n=0..50); # Wesley Ivan Hurt, Apr 22 2016

Mathematica

LinearRecurrence[{4,-6,4,-1},{1,31,177,535},50]
CoefficientList[Series[(1 + 27*x + 59*x^2 + 9*x^3)/(1 - x)^4, {x, 0, 30}], x] (* Wesley Ivan Hurt, Apr 22 2016 *)

PARI

vector(100, n, n--; 16*n^3+10*n^2+4*n+1) \\ Altug Alkan, Apr 22 2016

Formula

O.g.f.: (1+27*x+59*x^2+9*x^3)/(1-x)^4.

E.g.f.: (1+30*x+58*x^2+16*x^3)*exp(x).

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

a(n) = A158187(n) + A144965(n).