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A135963
a(n) = binomial(floor(n*(sqrt(5)+3)/2), n) for n>=0.
2
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
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 11 2007
STATUS
approved