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A149135 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), (-1, 1, 0), (0, 0, -1), (1, 0, 1)} 0
1, 1, 4, 9, 34, 114, 406, 1503, 5592, 21416, 83928, 327244, 1301822, 5202586, 20956424, 85286483, 347725526, 1426195886, 5880016708, 24319110834, 101086632952, 421341186950, 1760919637296, 7383805810480, 31031856064342, 130759597487428, 552246295418526, 2336493297695446, 9905532551587586 (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, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A149132 A149133 A149134 * A149136 A006392 A179079

Adjacent sequences:  A149132 A149133 A149134 * A149136 A149137 A149138

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified May 21 03:13 EDT 2022. Contains 353886 sequences. (Running on oeis4.)