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
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Nov 10 2013
STATUS
approved