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A148191 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, 0, 1), (0, 1, -1), (0, 1, 0), (1, -1, 0)} 0
1, 1, 2, 4, 12, 31, 91, 288, 940, 3099, 10607, 37862, 134767, 490159, 1826803, 6870465, 26029551, 100186211, 390244176, 1525584938, 6022917327, 24022355598, 96252798082, 387763662137, 1574666317612, 6428731348930, 26336898559556, 108517986685355, 449469203453607, 1867377245920794 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..29.

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, 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: A151434 A296292 A287966 * A141312 A148192 A192531

Adjacent sequences:  A148188 A148189 A148190 * A148192 A148193 A148194

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified May 31 09:30 EDT 2020. Contains 334748 sequences. (Running on oeis4.)