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Search: id:A149794
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| A149794 |
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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, 0, 0), (-1, 0, 1), (1, -1, 0), (1, 0, -1), (1, 1, 1)} |
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+0
1
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| 1, 1, 5, 19, 85, 343, 1603, 6963, 33103, 149467, 717119, 3310881, 15990331, 74956235, 363784547, 1724083341, 8397896787, 40123660477, 195991475917, 942221083739, 4612881371411, 22284361531757, 109301035545679, 530088616172357, 2604008059060621, 12669278896916643, 62317786772675273, 303997611988662661
(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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A149791 A149792 A149793 this_sequence A149795 A149796 A005191
Adjacent sequences: A149791 A149792 A149793 this_sequence A149795 A149796 A149797
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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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