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

0,2

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).

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).

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 *)

Crossrefs

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

Sequence in context: A098051 A329053 A084637 * A325917 A210542 A141366

Adjacent sequences: A100134 A100135 A100136 * A100138 A100139 A100140

Keyword

easy,nonn

Author

Paul Barry, Nov 06 2004

Status

approved