A107904 Expansion of (1+6x)/(1-12x^2).

1, 6, 12, 72, 144, 864, 1728, 10368, 20736, 124416, 248832, 1492992, 2985984, 17915904, 35831808, 214990848, 429981696, 2579890176, 5159780352, 30958682112, 61917364224, 371504185344, 743008370688, 4458050224128, 8916100448256, 53496602689536, 106993205379072

Offset: 0

Author

Paul Barry, May 27 2005

Keywords

• easy
• nonn

Comments

Fourth binomial transform is A107903.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,12).

Crossrefs

Cf. A094015, A107903, A108411.

Programs

Mathematica

LinearRecurrence[{0,12},{1,6},30] (* Harvey P. Dale, Sep 22 2014 *)

Formula

a(n) = ((1+sqrt(3))*(2*sqrt(3))^n + (1-sqrt(3))*(-2*sqrt(3))^n)/2.

a(2n) = 12^n, a(2n+1) = 6*12^n.

a(n) = 2^n*A108411(n+1). - R. J. Mathar, Aug 15 2023

From Amiram Eldar, Dec 06 2024: (Start)

Sum_{n>=0} 1/a(n) = 14/11.

Sum_{n>=0} (-1)^n/a(n) = 10/11. (End)