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Search: id:A148790
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| A148790 |
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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, 0), (1, -1, 0), (1, 0, 1), (1, 1, -1)} |
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+0
1
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| 1, 1, 3, 8, 25, 77, 257, 853, 2946, 10178, 36005, 127635, 459307, 1657395, 6042087, 22089132, 81346477, 300383933, 1115251580, 4151032922, 15515158110, 58122268630, 218459019113, 822782085889, 3107215915981, 11755843600909, 44576827929909, 169308082883825, 644271153070229, 2455271638906533
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Also, number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, 1), (0, -1), (0, 1), (1, 1)}
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LINKS
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A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
M. Bouquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
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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, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, 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: A022553 A148789 A088327 this_sequence A148791 A148792 A007563
Adjacent sequences: A148787 A148788 A148789 this_sequence A148791 A148792 A148793
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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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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 28 2008 at the suggestion of R. J. Mathar
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