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A150903 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, 0, 1), (-1, 1, 0), (1, 0, 0), (1, 1, 1)} 0
1, 2, 9, 29, 137, 504, 2437, 9552, 46795, 190432, 939661, 3920239, 19422969, 82481518, 409697827, 1763172523, 8773074029, 38151730972, 190064027439, 833520544825, 4156039712355, 18353203524932, 91569287436643, 406741687231426, 2030302712676439, 9063524526516028, 45257837046113369, 202911518359366177 (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, j, k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, j, -1 + 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: A280853 A268568 A150902 * A151306 A150904 A122675

Adjacent sequences:  A150900 A150901 A150902 * A150904 A150905 A150906

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified January 25 09:50 EST 2022. Contains 350565 sequences. (Running on oeis4.)