A100138 a(n) = Sum_{k=0..floor(n/6)} C(n-3k,3k) * 2^(n-5k).

1, 2, 4, 8, 16, 32, 66, 144, 336, 832, 2144, 5632, 14852, 38968, 101312, 260736, 664704, 1681152, 4226056, 10578080, 26407648, 65838848, 164095360, 409129472, 1020795408, 2549137824, 6371133120, 15935185792, 39878810624, 99837958144

Offset: 0

Author

Paul Barry, Nov 06 2004

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A052101, A100132, A100134, A100137, A100139.

Programs

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 *)

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).