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Search: id:A150922
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| A150922 |
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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), (1, 1, 0), (1, 1, 1)} |
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+0
1
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| 1, 2, 9, 33, 145, 624, 2777, 12580, 57449, 265178, 1235249, 5773663, 27205297, 128532068, 610043031, 2905567631, 13872723321, 66445225624, 318888929063, 1533775755417, 7391812386253, 35678828305288, 172511284953025, 835234120581390, 4049263838179501, 19655582161153286, 95512105686258709
(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, 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: A073400 A048498 A150921 this_sequence A150923 A150924 A150925
Adjacent sequences: A150919 A150920 A150921 this_sequence A150923 A150924 A150925
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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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