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A148360 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, 0, 1), (-1, 1, 1), (0, 1, -1), (0, 1, 0), (1, -1, 0)} 0
1, 1, 2, 5, 15, 46, 156, 550, 2012, 7606, 29449, 116379, 468297, 1911897, 7907479, 33074959, 139692623, 595163091, 2555275568, 11046348101, 48049939121, 210177221656, 924005069621, 4080977703387, 18099984139140, 80587248455206, 360075457598216, 1614132248554453, 7257668963955514 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A047086 A071731 A268648 * A148361 A346521 A148362

Adjacent sequences:  A148357 A148358 A148359 * A148361 A148362 A148363

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified May 18 02:30 EDT 2022. Contains 353779 sequences. (Running on oeis4.)