A241496 Expansion of (1 + 4*x + x^2) / (1 - x^2)^3.

1, 4, 4, 12, 9, 24, 16, 40, 25, 60, 36, 84, 49, 112, 64, 144, 81, 180, 100, 220, 121, 264, 144, 312, 169, 364, 196, 420, 225, 480, 256, 544, 289, 612, 324, 684, 361, 760, 400, 840, 441, 924, 484, 1012, 529, 1104, 576, 1200, 625, 1300, 676, 1404, 729, 1512

Offset: 0

Author

Stefano Maruelli, Apr 24 2014

Keywords

• nonn
• easy

Comments

Column 3 of the table in A229834.

Links

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

Crossrefs

Cf. A001082, A229834.

Cf. A171920: a(2k) = A000290(k+1); A046092: a(2k+1)= A046092(k+1).

Programs

Mathematica

Table[(3 n (n + 4) - (-1)^n (n (n + 4) + 2) + 10)/8, {n, 0, 60}] (* Bruno Berselli, Apr 24 2014 *)
LinearRecurrence[{0,3,0,-3,0,1},{1,4,4,12,9,24},60] (* Harvey P. Dale, Nov 25 2016 *)

Formula

G.f.: (1 + 4*x + x^2) / (1 - x^2)^3. [Bruno Berselli, Apr 24 2014]

a(n) = a(-n-4) = 1 + ( 3*n*(n + 4) + 2 - (-1)^n*(n*(n + 4) + 2) )/8. [Bruno Berselli, Apr 24 2014]

Extensions

Edited by Bruno Berselli, Apr 24 2014