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Search: id:A149810
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| A149810 |
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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), (0, 1, 0), (1, 0, 0)} |
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+0
1
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| 1, 2, 4, 10, 26, 66, 194, 590, 1742, 5490, 17402, 53538, 175010, 578366, 1865414, 6257594, 21029690, 68978514, 235163458, 805792730, 2705063098, 9347746654, 32323281142, 109506506322, 381914855922, 1335669367586, 4588435639362, 16136883499258, 56759236951130, 196105943366726, 693811296466158, 2458751902365166
(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, k, -1 + n] + aux[i, -1 + j, 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: A090032 A090377 A151278 this_sequence A095337 A162533 A052995
Adjacent sequences: A149807 A149808 A149809 this_sequence A149811 A149812 A149813
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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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