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Search: id:A149655
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| A149655 |
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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, 1, 1), (1, -1, 1), (1, 1, -1), (1, 1, 1)} |
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+0
1
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| 1, 1, 5, 15, 75, 289, 1445, 6095, 30475, 135117, 675585, 3087987, 15439935, 72008619, 360043095, 1703029437, 8515147185, 40694381623, 203471908115, 979988489573, 4899942447865, 23742016308033, 118710081540165, 577930415357795, 2889652076788975, 14121788791089079, 70608943955445395, 346141784385418635
(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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A101553 A149653 A149654 this_sequence A032122 A064678 A088935
Adjacent sequences: A149652 A149653 A149654 this_sequence A149656 A149657 A149658
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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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