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Search: id:A148452
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| A148452 |
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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, 0, 1), (1, 1, -1)} |
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+0
1
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| 1, 1, 2, 6, 17, 51, 173, 575, 2019, 7243, 26322, 97884, 367911, 1400005, 5389926, 20912874, 81885031, 322824487, 1281038396, 5114281062, 20522900399, 82766997179, 335260408347, 1363570222423, 5566956645365, 22806255720589, 93734432354154, 386403758136640, 1597338230149405, 6620451269940699
(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[i, 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: A157002 A071717 A148451 this_sequence A148453 A097514 A108630
Adjacent sequences: A148449 A148450 A148451 this_sequence A148453 A148454 A148455
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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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