A375273 Expansion of 1/(1 - 2*x - 3*x^2 - 4*x^3 + 4*x^4).

1, 2, 7, 24, 73, 238, 763, 2436, 7821, 25050, 80255, 257200, 824081, 2640582, 8461187, 27111644, 86872853, 278363058, 891946503, 2858027016, 9157854361, 29344123550, 94026132235, 301283944500, 965391362461, 3093362593162, 9911930522767, 31760378496864

Offset

0,2

Links

Table of n, a(n) for n=0..27.

Index entries for linear recurrences with constant coefficients, signature (2,3,4,-4).

Formula

a(n) = 2*a(n-1) + 3*a(n-2) + 4*a(n-3) - 4*a(n-4).

a(n) = (1/2) * Sum_{k=0..floor(n/2)} 2^k * binomial(2*n-2*k+2,2*k+1).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-2*x-3*x^2-4*x^3+4*x^4))
(PARI) a(n) = sum(k=0, n\2, 2^k*binomial(2*n-2*k+2, 2*k+1))/2;

Crossrefs

Cf. A182890, A375255.

Cf. A108480, A108488.

Sequence in context: A082047 A370306 A341803 * A272483 A129020 A024024

Adjacent sequences: A375270 A375271 A375272 * A375274 A375275 A375276

Keyword

nonn

Author

Seiichi Manyama, Aug 09 2024

Status

approved