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A148331 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, 0), (-1, 1, -1), (0, 0, 1), (1, -1, 0), (1, 1, -1)} 0
1, 1, 2, 5, 14, 42, 137, 464, 1626, 5882, 21677, 81732, 313304, 1212616, 4773498, 18989434, 75930374, 307605618, 1255603937, 5139250646, 21254360832, 88416763064, 368323147150, 1547315926686, 6531070849774, 27584038509482, 117317585175507, 500936901965294, 2139262376029736 (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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A148330 A149876 A165146 * A306422 A052853 A149877

Adjacent sequences:  A148328 A148329 A148330 * A148332 A148333 A148334

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified May 23 23:42 EDT 2022. Contains 353993 sequences. (Running on oeis4.)