A051494 Expansion of (1 - x + x^2 + x^3)/(1 - x^2)^3.

1, -1, 4, -2, 9, -3, 16, -4, 25, -5, 36, -6, 49, -7, 64, -8, 81, -9, 100, -10, 121, -11, 144, -12, 169, -13, 196, -14, 225, -15, 256, -16, 289, -17, 324, -18, 361, -19, 400, -20, 441, -21, 484, -22, 529, -23, 576, -24, 625, -25, 676, -26, 729, -27, 784, -28, 841, -29, 900, -30

Offset

0,3

Comments

Or, n^2 followed by -n. - Mohammad K. Azarian, Aug 29 2005

Also, +-A000217(m) + A000217(m-1) = 1+0, -1+0, 3+1, -3+1, 6+3, -6+3, ..., for m > 0. - Bruno Berselli, Jun 07 2013

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

Formula

a(n) = (n^2 + 2*n + 2 + (n^2 + 6*n + 6)*(-1)^n)/8. - Bruno Berselli, Jun 07 2013

Mathematica

LinearRecurrence[{0, 3, 0, -3, 0, 1}, {1, -1, 4, -2, 9, -3}, 60] (* Bruno Berselli, Jun 07 2013 *)
CoefficientList[Series[(1 - x + x^2 + x^3) / (1 - x^2)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 19 2013 *)

Prog

(Magma) /* By the second comment: */ A000217:=func<i | i*(i+1)/2>; [s*A000217(n)+A000217(n-1): s in [1, -1], n in [1..30]]; // Bruno Berselli, Jun 07 2013

Crossrefs

Sequence in context: A075594 A076022 A064421 * A262025 A118013 A157647

Adjacent sequences: A051491 A051492 A051493 * A051495 A051496 A051497

Keyword

sign,easy

Author

N. J. A. Sloane

Status

approved