A100139 a(n) = Sum_{k=0..floor(n/6)} C(n-3k,3k) * 3^k * 2^(n-6k).

1, 2, 4, 8, 16, 32, 67, 152, 376, 992, 2704, 7424, 20233, 54398, 144112, 376736, 974368, 2500544, 6385435, 16264220, 41396788, 105423776, 268818064, 686499008, 1755723793, 4495691834, 11521647916, 29543647160, 75774096832, 194353495424

Offset: 0

Author

Paul Barry, Nov 06 2004

Keywords

• easy
• nonn

Comments

Binomial transform of 1,1,1,1,1,1,4,4,13,13,31,... with g.f. (1-x)^2(1+x)^3/(1-3x^2+3x^4-4x^6)=(1+x)(1-x^2)^2/((1-x^2)^3-3x^6).

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-12,8,0,0,3).

Crossrefs

Cf. A097122, A100133, A100134, A100137, A100138.

Programs

Mathematica

LinearRecurrence[{6,-12,8,0,0,3},{1,2,4,8,16,32},30] (* Harvey P. Dale, Sep 30 2015 *)

Formula

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

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