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A148299 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, 0), (-1, 1, 1), (0, 0, 1), (1, 0, -1)} 0
1, 1, 2, 5, 13, 36, 116, 368, 1232, 4246, 14725, 52621, 191368, 702694, 2623720, 9865742, 37418929, 143465704, 553471257, 2151274776, 8414169759, 33058543852, 130629116341, 518625570150, 2067756813513, 8279716018983, 33265741928635, 134107475463383, 542469971348673, 2200776384598785 (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, j, 1 + 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] + 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: A148296 A148297 A148298 * A148300 A038982 A266966

Adjacent sequences:  A148296 A148297 A148298 * A148300 A148301 A148302

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified July 18 11:30 EDT 2019. Contains 325138 sequences. (Running on oeis4.)