A135963 a(n) = binomial(floor(n*(sqrt(5)+3)/2), n) for n>=0.

1, 2, 10, 35, 210, 1287, 5005, 31824, 125970, 817190, 5311735, 21474180, 141120525, 927983760, 3796297200, 25140840660, 103077446706, 686353797976, 4568648125690, 18851684897584, 125994627894135, 520341450264090

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = binomial(A001950(n), A000201(n)), where A001950(n) = floor(n*phi^2) and A000201(n) = floor(n*phi) are the upper and lower Wythoff sequences, respectively, with phi = (sqrt(5)+1)/2.

Prog

(PARI) a(n)=binomial(floor(n*(sqrt(5)+3)/2), n)
(PARI) {a(n)=local(phi=(sqrt(5)+1)/2); binomial(floor(n*phi^2), floor(n*phi))}
(Python)
from math import isqrt, comb
def A135963(n): return comb(n+(n+isqrt(5*n**2)>>1), n) # Chai Wah Wu, Aug 10 2022

Crossrefs

Cf. A135962; A001950, A000201.

Sequence in context: A220255 A146983 A327075 * A140954 A309889 A155894

Adjacent sequences: A135960 A135961 A135962 * A135964 A135965 A135966

Keyword

nonn

Author

Paul D. Hanna, Dec 11 2007

Status

approved