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A302180 Number of 3D walks of type aad. 0
1, 1, 3, 7, 23, 71, 251, 883, 3305, 12505, 48895, 193755, 783355, 3205931, 13302329, 55764413, 236174933, 1008773269, 4343533967, 18834033443, 82201462251, 360883031291, 1592993944723, 7066748314147, 31493800133173, 140953938878821, 633354801073571 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
See Dershowitz (2017) for precise definition.
Number of 3D walks of length n in the first octant using steps (1, 1, 0), (1, -1, 0), (1, 0, 1), (1, 0, -1) and (1, 0, 0) that start at the origin and end at (n, 0, 0). The analogous problem in 2D is given by the Motzkin numbers A001006. - Farzan Byramji, Mar 06 2021
LINKS
Nachum Dershowitz, Touchard's Drunkard, Journal of Integer Sequences, Vol. 20 (2017), #17.1.5.
CROSSREFS
Sequence in context: A148702 A194691 A148703 * A045723 A140456 A066768
KEYWORD
nonn,walk,more
AUTHOR
N. J. A. Sloane, Apr 09 2018
EXTENSIONS
a(14)-a(26) from Farzan Byramji, Mar 06 2021
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)