A228843 a(n) = 4^n*A228842(n).

2, 24, 448, 9216, 192512, 4030464, 84410368, 1767899136, 37027315712, 775510032384, 16242492571648, 340187179646976, 7124972786941952, 149227367389200384, 3125458558976524288, 65460453902527758336, 1371021545886168645632, 28715048051506270961664

Offset: 0

Author

R. J. Mathar, Nov 10 2013

Keywords

• nonn
• easy

Comments

Bhadouria et al. call this the 4-binomial transform of the 4-Lucas sequence.

Binomial transform of the binomial transform of the binomial transform of A087215.

Links

• Colin Barker, Table of n, a(n) for n = 0..750
• P. Bhadouria, D. Jhala, B. Singh, Binomial Transforms of the k-Lucas Sequences and its Properties, The Journal of Mathematics and Computer Science (JMCS), Volume 8, Issue 1, Pages 81-92; sequence T_4.
• Index entries for linear recurrences with constant coefficients, signature (24,-64).

Programs

Mathematica

LinearRecurrence[{24,-64},{2,24},20] (* Harvey P. Dale, Jul 04 2022 *)

PARI

Vec(2*(1 - 12*x) / (1 - 24*x + 64*x^2 ) + O(x^30)) \\ Colin Barker, Sep 23 2017

Formula

G.f.: 2*( 1-12*x ) / ( 1-24*x+64*x^2 ).

a(n) = 2*A098647(n).

a(n) = A000302(n)*A228842(n). - Omar E. Pol, Nov 10 2013

From Colin Barker, Sep 23 2017: (Start)

a(n) = 24*a(n-1) - 64*a(n-2) for n>1.

a(n) = (12-4*sqrt(5))^n + (4*(3+sqrt(5)))^n.

(End)