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Search: id:A148681
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| A148681 |
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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, 0), (-1, -1, 1), (-1, 0, -1), (0, 1, -1), (1, 0, 1)} |
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+0
1
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| 1, 1, 3, 7, 22, 66, 227, 748, 2710, 9643, 35646, 133338, 506112, 1938692, 7546335, 29463016, 116453080, 462871956, 1851092051, 7451911578, 30144766089, 122486787548, 500198189286, 2049540237382, 8430872633779, 34799109527697, 144055056806443, 598143461783294, 2490167439891266
(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, -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] + aux[1 + i, 1 + 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: A036719 A166135 A007595 this_sequence A148682 A148683 A148684
Adjacent sequences: A148678 A148679 A148680 this_sequence A148682 A148683 A148684
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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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