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Search: id:A150228
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| A150228 |
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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, -1), (-1, 0, 0), (0, -1, 0), (0, 0, 1), (1, 1, 0)} |
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+0
1
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| 1, 2, 6, 22, 78, 298, 1196, 4776, 19630, 82460, 346174, 1475372, 6366272, 27477314, 119705140, 525695678, 2309607508, 10211810684, 45406121298, 201982264656, 902651784780, 4050830854290, 18186197331954, 81934870356650, 370339304893844, 1674510493383670, 7592425912834458, 34513742317591202
(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, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, 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}]
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CROSSREFS
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Sequence in context: A107239 A148496 A106434 this_sequence A072547 A150229 A150230
Adjacent sequences: A150225 A150226 A150227 this_sequence A150229 A150230 A150231
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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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