OFFSET
0,2
COMMENTS
Binomial transform of 1,1,1,1,1,1,3,3,9,9,21,... with g.f. (1-x)^2(1+x)^2/(1-3x^2+3x^4-3x^6)=(1+x)(1-x^2)^2/((1-x^2)^3-2x^6).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-12,8,0,0,2).
FORMULA
G.f.: (1-2x)^2/((1-2x)^3 - 2x^6).
a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3) + 2*a(n-6).
MATHEMATICA
Table[Sum[Binomial[n-3k, 3k]2^(n-5k), {k, 0, Floor[n/6]}], {n, 0, 30}] (* or *) LinearRecurrence[{6, -12, 8, 0, 0, 2}, {1, 2, 4, 8, 16, 32}, 30] (* Harvey P. Dale, Dec 30 2019 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Nov 06 2004
STATUS
approved