OFFSET
0,2
COMMENTS
Binomial transform of 1,1,1,1,3,3,7,7,41,... (g.f. (1-x)(1+x)^2/(1-2x^2-x^4)).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-4,0,2)
FORMULA
G.f.: (1-2x)/((1-2x)^2-2x^4).
a(n) = 4*a(n-1) - 4*a(n-2) + 2*a(n-3).
a(n) = Sum_{k=0..floor(n/2)} C(n-k, k)2^(n-3k/2)(1+(-1)^k)/2. - Paul Barry, Jan 22 2005
MATHEMATICA
LinearRecurrence[{4, -4, 0, 2}, {1, 2, 4, 8}, 30] (* Harvey P. Dale, Jun 07 2016 *)
PROG
(PARI) a(n) = sum(k=0, n\4, binomial(n-2*k, 2*k)*2^(n-3*k)); \\ Michel Marcus, Oct 09 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Nov 06 2004
STATUS
approved