A108486 Sum binomial(2n-2k,2k)3^k*2^(n-k), k=0..floor(n/2).

1, 2, 10, 80, 412, 2456, 14680, 85376, 503056, 2959136, 17381536, 102199040, 600757696, 3531251072, 20758107520, 122021457920, 717273440512, 4216334967296, 24784750512640, 145691471876096, 856414086962176

Offset: 0

Author

Paul Barry, Jun 04 2005

Keywords

• easy
• nonn

Comments

In general, sum{k=0..floor(n/2), C(2n-2k,2k)a^k*b^(n-k)} has expansion (1-bx-abx^2)/(1-2bx-(2ab-b^2)x^2-2ab^2*x^3+(ab)^2*x^4).

Links

• Index entries for linear recurrences with constant coefficients, signature (4,8,24,-36).

Formula

G.f.: (1-2x-6x^2)/(1-4x-8x^2-24x^3+36x^4); a(n)=4a(n-1)+8a(n-2)+24a(n-3)-36a(n-4).