Revision History for A148401
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A148401
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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), (0, 1, -1), (0, 1, 0), (1, -1, 1)}.
(history;
published version)
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#4 by Wesley Ivan Hurt at Mon Jan 01 00:54:21 EST 2024
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#3 by Wesley Ivan Hurt at Mon Jan 01 00:54:19 EST 2024
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| NAME
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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), (0, 1, -1), (0, 1, 0), (1, -1, 1)})}.
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| STATUS
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approved
editing
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#2 by Russ Cox at Fri Mar 30 18:54:04 EDT 2012
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| AUTHOR
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_Manuel Kauers (manuel(AT)kauers.de), _, Nov 18 2008
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Discussion
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Fri Mar 30
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| OEIS Server: https://oeis.org/edit/global/269
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#1 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009
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| NAME
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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), (0, 1, -1), (0, 1, 0), (1, -1, 1)}
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| DATA
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1, 1, 2, 5, 17, 49, 175, 574, 2215, 7794, 31002, 114827, 469571, 1802223, 7507304, 29616634, 125224110, 504660980, 2158999665, 8852141829, 38237746911, 159011512866, 692421182858, 2913714414087, 12774870975808, 54299529666488, 239474510946361, 1026713175859252, 4551287121301993
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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, <a href="http://arxiv.org/abs/0811.2899">ArXiv 0811.2899</a>.
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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, -1 + j, k, -1 + n] + aux[i, -1 + 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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| 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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| STATUS
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approved
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