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A148726 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, 1), (-1, 0, 1), (0, 1, -1), (0, 1, 1), (1, 0, -1)} 0
1, 1, 3, 7, 25, 72, 278, 916, 3672, 13025, 53751, 200217, 843672, 3257716, 13933910, 55297282, 239315186, 970147542, 4239127095, 17480675840, 76987864204, 321968327531, 1427398289337, 6040117766051, 26929613280450, 115096541374645, 515667082927505, 2222925099783314, 10001975287742135 (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, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A332508 A309911 A148725 * A148727 A148728 A148729

Adjacent sequences:  A148723 A148724 A148725 * A148727 A148728 A148729

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified August 5 17:36 EDT 2021. Contains 346488 sequences. (Running on oeis4.)