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A051494 Expansion of (1-x+x^2+x^3)/(1-x^2)^3. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 22 18:55 EDT 2018. Contains 316500 sequences. (Running on oeis4.)