Revision History for A149266
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| A149266
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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, 0, 0), (0, -1, 1), (1, 0, -1), (1, 1, 0)}.
(history;
published version)
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#4 by Wesley Ivan Hurt at Thu Dec 28 20:22:26 EST 2023
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#3 by Wesley Ivan Hurt at Thu Dec 28 20:22:24 EST 2023
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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, 1), (-1, 0, 0), (0, -1, 1), (1, 0, -1), (1, 1, 0)})}.
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approved
editing
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#2 by Russ Cox at Fri Mar 30 18:54:11 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, 1), (-1, 0, 0), (0, -1, 1), (1, 0, -1), (1, 1, 0)}
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| DATA
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1, 1, 4, 11, 40, 145, 557, 2204, 8878, 36670, 153158, 649421, 2779083, 12009927, 52301065, 229322103, 1011602788, 4485941698, 19989047298, 89445085086, 401786301272, 1811068535817, 8189394966213, 37138317913733, 168865708226573, 769695000793202, 3516190063129191, 16096483440690982
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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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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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| 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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