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A150902 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, -1), (-1, -1, 0), (-1, 0, 0), (1, 1, 0), (1, 1, 1)} 0
1, 2, 9, 29, 137, 504, 2427, 9514, 46279, 188378, 922011, 3848325, 18913895, 80375284, 396204897, 1706671449, 8431581777, 36707170694, 181657234959, 797648512851, 3952774138035, 17479357325268, 86714636143797, 385735383724232, 1915353194522889, 8563284203023746, 42552753012103537, 191079601486952819 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..27.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

MATHEMATICA

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n] + aux[1 + i, 1 + j, 1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

CROSSREFS

Sequence in context: A183383 A280853 A268568 * A150903 A151306 A150904

Adjacent sequences:  A150899 A150900 A150901 * A150903 A150904 A150905

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified January 23 13:57 EST 2022. Contains 350511 sequences. (Running on oeis4.)