Revision History for A148959
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| A148959
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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, 0, 0), (0, -1, 0), (0, 1, 1), (1, 1, -1)}.
(history;
published version)
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#4 by Wesley Ivan Hurt at Fri Mar 29 19:46:19 EDT 2024
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#3 by Wesley Ivan Hurt at Fri Mar 29 19:46:18 EDT 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, 0, 0), (0, -1, 0), (0, 1, 1), (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 18:54:09 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
| 18:54
| 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, 0, 0), (0, -1, 0), (0, 1, 1), (1, 1, -1)}
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| DATA
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1, 1, 3, 9, 31, 100, 370, 1372, 5290, 20266, 80361, 321735, 1307984, 5335667, 22024808, 91659114, 384509857, 1620023737, 6864307125, 29248903041, 125269708719, 538502958487, 2323193194405, 10060821504853, 43727466779310, 190618286246040, 833147784737097, 3651348013005285, 16045299842617819
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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, -1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, 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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