A168297 a(n) = n^3 + (1-n)^2.

1, 1, 9, 31, 73, 141, 241, 379, 561, 793, 1081, 1431, 1849, 2341, 2913, 3571, 4321, 5169, 6121, 7183, 8361, 9661, 11089, 12651, 14353, 16201, 18201, 20359, 22681, 25173, 27841, 30691, 33729, 36961, 40393, 44031, 47881, 51949, 56241, 60763, 65521

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: (1 - 3*x + 11*x^2 - 3*x^3)/(1-x)^4. - R. J. Mathar, Nov 24 2009

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - G. C. Greubel, Jul 17 2016

Mathematica

Table[n^3 + (1 - n)^2, {n, 0, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 1, 9, 31}, 50] (* G. C. Greubel, Jul 17 2016 *)

Prog

(Magma) [n^3+(1-n)^2: n in [0..40]]; // Vincenzo Librandi, Jul 18 2016
(PARI) a(n)=n^3+(n-1)^2 \\ Charles R Greathouse IV, Oct 18 2022

Crossrefs

Cf. A153257.

Sequence in context: A133739 A266397 A288419 * A004126 A344675 A177342

Adjacent sequences: A168294 A168295 A168296 * A168298 A168299 A168300

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Nov 22 2009

Extensions

Flipped/normalized the sign of n - R. J. Mathar, Nov 24 2009

Further edited by N. J. A. Sloane, Nov 24 2009

Status

approved