A302188 Number of 3D walks of type bce.

1, 3, 12, 53, 252, 1252, 6416, 33609, 178996, 965660, 5263728, 28936404, 160204336, 892313424, 4995832640, 28096475977, 158638993476, 898844200524, 5108695394096, 29117034808980, 166370716319088, 952789631705104, 5467881256289856, 31438798094242244, 181079794531199440, 1044651995141484912

Offset

0,2

Comments

See Dershowitz (2017) for precise definition.

Binomial transform of A150500 (Number of 3D walks of type bcd). - Mélika Tebni, Nov 28 2024

Links

Table of n, a(n) for n=0..25.

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

Prog

(Python)
from math import comb as binomial
def a(n):
    return sum(binomial(n, k)*sum(binomial(k, j)*binomial(j, j//2)**2 for j in range(k+1)) for k in range(n+1))
print([a(n) for n in range(26)]) # Mélika Tebni, Nov 28 2024

Crossrefs

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

Sequence in context: A110122 A378467 A307412 * A060460 A306525 A293131

Adjacent sequences: A302185 A302186 A302187 * A302189 A302190 A302191

Keyword

nonn,walk

Author

N. J. A. Sloane, Apr 09 2018

Extensions

a(12)-a(25) from Mélika Tebni, Nov 28 2024

Status

approved