A162466 a(n) = 12*a(n-2) for n > 2; a(1) = 1, a(2) = 8.

1, 8, 12, 96, 144, 1152, 1728, 13824, 20736, 165888, 248832, 1990656, 2985984, 23887872, 35831808, 286654464, 429981696, 3439853568, 5159780352, 41278242816, 61917364224, 495338913792, 743008370688, 5944066965504

Offset: 1

Author

Klaus Brockhaus, Jul 04 2009

Keywords

• nonn

Comments

Eighth binomial transform is A161729.

Links

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

Crossrefs

Cf. A161729, A161728, A162436, A162272, A074324.

Programs

Mathematica

LinearRecurrence[{0,12},{1,8},30] (* Harvey P. Dale, Sep 17 2020 *)

PARI

{m=24; v=concat([1, 8], vector(m-2)); for(n=3, m, v[n]=12*v[n-2]); v}

PARI

Vec(x*(1+8*x)/(1-12*x^2)+O(x^29)) \\ M. F. Hasler, Dec 03 2014

Formula

a(n) = (5-(-1)^n)*2^(1/2 *(2*n-3+(-1)^n))*3^(1/4*(2*n-5+(-1)^n)).

G.f.: x*(1+8*x)/(1-12*x^2).

a(n) = 2^(n-1)*A074324(n). - M. F. Hasler, Dec 03 2014

Extensions

G.f. and comment corrected, formula added by Klaus Brockhaus, Sep 18 2009