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A148287 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, 0, -1), (0, 1, -1), (1, 0, 0)}. 0
1, 1, 2, 5, 12, 35, 107, 329, 1096, 3749, 12891, 46265, 169259, 620390, 2337429, 8934790, 34152776, 133143500, 524875592, 2067248994, 8264941659, 33337264862, 134285940718, 547393149232, 2247487271913, 9213311703539, 38138609281747, 158824698192248, 660317459502835, 2767794642935800 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
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, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A075203 A075205 A054359 * A036357 A000104 A342537
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified February 26 15:44 EST 2024. Contains 370352 sequences. (Running on oeis4.)