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A148349 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, 1, -1), (1, -1, 0), (1, -1, 1), (1, 0, 1)}. 0
1, 1, 2, 5, 15, 40, 134, 415, 1432, 4780, 17358, 59964, 225359, 805190, 3084375, 11331471, 44080172, 165262446, 651653671, 2482120277, 9895945289, 38203217093, 153666804970, 600090569568, 2431881674131, 9589685348451, 39116379168674, 155536622339373, 638049144003842, 2555525820704081 (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, -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, 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: A309299 A151260 A148348 * A076865 A190140 A006649
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified February 26 13:34 EST 2024. Contains 370352 sequences. (Running on oeis4.)