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Search: id:A148100
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| A148100 |
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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, 1), (0, -1, 1), (0, 1, -1), (1, 0, 0)} |
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+0
1
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| 1, 1, 2, 4, 10, 26, 76, 239, 753, 2540, 8572, 30128, 106501, 387844, 1422789, 5316121, 20099588, 76671429, 296355338, 1151184226, 4524804463, 17853802855, 71134139857, 284557313732, 1146559570375, 4641910594671, 18885060480277, 77240337339152, 316960064504831, 1307542974531887, 5407643110588584
(list; graph; listen)
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OFFSET
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0,3
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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, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + 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}]
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CROSSREFS
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Sequence in context: A007580 A000085 A047653 this_sequence A149815 A149816 A149817
Adjacent sequences: A148097 A148098 A148099 this_sequence A148101 A148102 A148103
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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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