A153257 a(n) = n^3 - (n+1)^2.

-1, -3, -1, 11, 39, 89, 167, 279, 431, 629, 879, 1187, 1559, 2001, 2519, 3119, 3807, 4589, 5471, 6459, 7559, 8777, 10119, 11591, 13199, 14949, 16847, 18899, 21111, 23489, 26039, 28767, 31679, 34781, 38079, 41579, 45287, 49209, 53351, 57719, 62319, 67157, 72239

Offset

0,2

Links

Table of n, a(n) for n=0..42.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

From Elmo R. Oliveira, Aug 27 2025: (Start)

G.f.: (-1 + x + 5*x^2 + x^3)/(1 - x)^4.

E.g.f.: (-1 + x)*(1 + 3*x + x^2)*exp(x).

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

Mathematica

Table[n^3-(n+1)^2, {n, 0, 40}] (* Harvey P. Dale, Oct 05 2022 *)

Prog

(PARI) my(x='x+O('x^43)); Vec((x^3+5*x^2+x-1)/(x-1)^4) \\ Elmo R. Oliveira, Aug 27 2025

Crossrefs

Cf. A045991, A069778, A081437, A140719.

Sequence in context: A228534 A119908 A362996 * A002185 A002589 A048522

Adjacent sequences: A153254 A153255 A153256 * A153258 A153259 A153260

Keyword

sign,easy

Author

Vladimir Joseph Stephan Orlovsky, Dec 22 2008

Extensions

More terms from Elmo R. Oliveira, Aug 27 2025

Status

approved