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Search: id:A150455
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| A150455 |
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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, 0, -1), (0, 0, 1), (1, -1, 0), (1, 1, 1)} |
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+0
1
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| 1, 2, 7, 25, 95, 384, 1581, 6650, 28445, 122882, 536461, 2362819, 10471121, 46690324, 209233801, 941662339, 4255508597, 19297965112, 87782900607, 400446990191, 1831345492367, 8394785864716, 38564102468327, 177499935969584, 818454683598331, 3780179695153546, 17486318321801777, 81004889051618285
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MATHEMATICA
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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[-1 + i, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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}]
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CROSSREFS
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Sequence in context: A116396 A150453 A150454 this_sequence A150456 A150457 A150458
Adjacent sequences: A150452 A150453 A150454 this_sequence A150456 A150457 A150458
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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