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Search: id:A150816
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| A150816 |
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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, 1), (0, -1, 1), (0, 1, -1), (0, 1, 1), (1, 0, 1)} |
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+0
1
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| 1, 2, 8, 31, 136, 590, 2693, 12262, 57207, 266993, 1262974, 5981798, 28565047, 136604608, 656810502, 3162420406, 15283892129, 73959776962, 358882669335, 1743380069204, 8486712994924, 41353150789775, 201831466011484, 985908774276470, 4822318632528052, 23604571997644201, 115665780530706013
(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, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + 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]]; 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: A150813 A150814 A150815 this_sequence A150817 A150818 A009567
Adjacent sequences: A150813 A150814 A150815 this_sequence A150817 A150818 A150819
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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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