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A150053 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), (0, 0, 1), (0, 1, 1), (1, 1, -1)}. 0
1, 2, 6, 18, 62, 210, 758, 2714, 10054, 37090, 139614, 524498, 1995606, 7587258, 29089670, 111524322, 430033118, 1658717458, 6424179254, 24893373562, 96748946886, 376241540642, 1466424281790, 5719018497394, 22342446655478, 87338376774970, 341874710908710, 1339005141036514, 5250116727074142 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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[i, -1 + j, -1 + k, -1 + n] + aux[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: A303117 A150052 A262590 * A150054 A067052 A150055
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified July 25 04:49 EDT 2024. Contains 374586 sequences. (Running on oeis4.)