A374598 Expansion of 1/sqrt(1 - 4*x - 8*x^3).

1, 2, 6, 24, 94, 372, 1508, 6192, 25638, 106908, 448356, 1889040, 7989676, 33902504, 144259944, 615330784, 2630199942, 11263613484, 48315367076, 207556060816, 892819376964, 3845161246424, 16578320962104, 71548426931616, 309070048163676, 1336223562436632

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

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

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x-8*x^3))
(PARI) a(n) = sum(k=0, n\3, 2^k*binomial(n-2*k, k)*binomial(2*(n-2*k), n-2*k));

Crossrefs

Cf. A157004, A360266.

Cf. A084609, A374599.

Sequence in context: A192466 A367274 A375276 * A361752 A115220 A293185

Adjacent sequences: A374594 A374595 A374596 * A374599 A374600 A374601

Keyword

nonn

Author

Seiichi Manyama, Jul 13 2024

Status

approved