A100137 a(n) = Sum_{k=0..floor(n/6)} C(n-3k,3k) * 2^(n-6k).

1, 2, 4, 8, 16, 32, 65, 136, 296, 672, 1584, 3840, 9473, 23566, 58736, 146080, 361760, 891328, 2184961, 5331476, 12958684, 31400160, 75910320, 183220800, 441787201, 1064687642, 2565404524, 6181873208, 14899796416, 35922756992, 86635757825

Offset: 0

Author

Paul Barry, Nov 06 2004

Keywords

• easy
• nonn

Comments

Binomial transform of 1,1,1,1,1,1,2,2,2,5,5,11,11,... with g.f. (1-x)^2(1+x)^2/(1-3x^2+3x^4-2x^6)=(1+x)(1-x^2)^2/((1-x^2)^3-x^6).

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-12,8,0,0,1).

Crossrefs

Cf. A024493, A100131, A100134, A100137, A100138.

Programs

Mathematica

Table[Sum[Binomial[n-3k,3k]2^(n-6k),{k,0,Floor[n/6]}],{n,0,30}] (* or *) LinearRecurrence[{6,-12,8,0,0,1},{1,2,4,8,16,32},31] (* Harvey P. Dale, Mar 19 2015 *)

Formula

G.f.: (1-2x)^2/((1-2x)^3 - x^6).

a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3) + a(n-6).