A380121 a(n) = C(n, Q(n+3, 4)-1)*C(n, Q(n+1, 4)) + C(n, Q(3*n+1, 4))*C(n, Q(3*n+3, 4)) where C = binomial and Q(x, y) = floor(x/y).

1, 2, 3, 6, 20, 50, 126, 294, 1008, 2592, 7425, 18150, 62920, 163592, 496860, 1242150, 4331600, 11328800, 35581680, 90140256, 315490896, 828163602, 2658338298, 6793531206, 23836951600, 62728820000, 204451146900, 525731520600, 1848025951200, 4872068416800, 16059866355000

Offset: 0

Author

Peter Luschny, Jan 17 2025

Keywords

• nonn

Comments

a(n) is the minimum of row n of A378067 except at n = 1.

Crossrefs

Cf. A378067.

Programs

Maple

a := n -> binomial(n, iquo(n+3, 4)-1) * binomial(n, iquo(n+1, 4)) + binomial(n, iquo(3*n+1, 4)) * binomial(n,iquo(3*n+3, 4)): seq(a(n), n = 0..29);

Python

from math import comb as C
def a(n): return C(n,(n+3)//4-1)*C(n,(n+1)//4)+C(n,(3*n+1)//4)*C(n,(3*n+3)//4) if n>0 else 1; print([a(n) for n in range(31)])