A241577 n^3 + 4*n^2 - 5*n + 1.

1, 1, 15, 49, 109, 201, 331, 505, 729, 1009, 1351, 1761, 2245, 2809, 3459, 4201, 5041, 5985, 7039, 8209, 9501, 10921, 12475, 14169, 16009, 18001, 20151, 22465, 24949, 27609, 30451, 33481, 36705, 40129, 43759, 47601, 51661, 55945, 60459, 65209, 70201, 75441, 80935, 86689, 92709, 99001, 105571, 112425, 119569

Offset: 0

Author

N. J. A. Sloane, Apr 27 2014

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Adalbert Kerber, A matrix of combinatorial numbers related to the symmetric groups, Discrete Math., 21 (1978), 319-321. See Eq. (7), col. 4.
• A. Kerber, A matrix of combinatorial numbers related to the symmetric groups<, Discrete Math., 21 (1978), 319-321. [Annotated scanned copy]
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Programs

Magma

[n^3+4*n^2-5*n+1: n in [0..50]]; // Vincenzo Librandi, Apr 28 2014

Mathematica

CoefficientList[Series[(1 - 3 x + 17 x^2 - 9 x^3)/(1 - x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Apr 28 2014 *)

PARI

a(n)=n^3+4*n^2-5*n+1 \\ Charles R Greathouse IV, Aug 26 2014

Formula

G.f.: (1-3*x+17*x^2-9*x^3)/(1-x)^4. - Vincenzo Librandi, Apr 28 2014

Recurrence: a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Fung Lam, May 11 2014