A302187 Number of 3D walks of type bcc.

1, 2, 8, 30, 138, 620, 3060, 14910, 76650, 390852, 2063376, 10832052, 58264668, 312123240, 1702423008, 9256786110, 51036229530, 280696824980, 1560925457520, 8663089672380, 48512836025940, 271229902496280, 1527733861191720, 8593482390429300, 48642125421855420, 275014629509319000

Offset: 0

Author

N. J. A. Sloane, Apr 09 2018

Keywords

• nonn
• walk

Comments

See Dershowitz (2017) for precise definition.

Links

• Nachum Dershowitz, Touchard's Drunkard, Journal of Integer Sequences, Vol. 20 (2017), #17.1.5.

Crossrefs

Cf. A000108, A000984, A002212, A002896, A005572, A026375, A064037, A081671, A138547, A145847, A145867, A150500, A202814.

Cf. A001405, A018224.

Programs

Python

from math import comb as binomial
def a(n):
    return sum(binomial(n, k)*binomial(k, k//2)*binomial(n-k, (n-k)//2)**2 for k in range(n+1))
print([a(n) for n in range(26)]) # Mélika Tebni, Nov 25 2024

Formula

a(n) = Sum_{k=0..n} binomial(n, k)*A001405(k)*A018224(n-k). - Mélika Tebni, Nov 25 2024

Extensions

a(12)-a(25) from Nachum Dershowitz, Aug 03 2020