A228568 a(n) = 2^n*A056236(n).

2, 8, 48, 320, 2176, 14848, 101376, 692224, 4726784, 32276480, 220397568, 1504968704, 10276569088, 70172803072, 479169871872, 3271976550400, 22342453428224, 152563815022592, 1041770892754944, 7113656621858816, 48575085832830976, 331691433687777280

Offset

0,1

Comments

Bhadouria et al. call this the 2-binomial transform of the 2-Lucas numbers.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

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_2.

Index entries for linear recurrences with constant coefficients, signature (8,-8).

Formula

G.f.: 2*( 1-4*x ) / ( 1-8*x+8*x^2 ).

a(n) = 2*A084130(n).

From Colin Barker, Mar 16 2016: (Start)

a(n) = ((4-2*sqrt(2))^n+(2*(2+sqrt(2)))^n).

a(n) = 8*a(n-1)-8*a(n-2) for n>1.

(End)

Prog

(PARI) Vec(2*(1-4*x)/(1-8*x+8*x^2) + O(x^50)) \\ Colin Barker, Mar 16 2016

Crossrefs

Sequence in context: A152661 A177066 A356429 * A007170 A355488 A379382

Adjacent sequences: A228565 A228566 A228567 * A228569 A228570 A228571

Keyword

nonn,easy

Author

R. J. Mathar, Nov 10 2013

Status

approved