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Search: id:A151319
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| A151319 |
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Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 0), (0, -1), (0, 1), (1, 0), (1, 1)} |
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+0
1
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| 1, 3, 13, 57, 263, 1233, 5869, 28201, 136471, 664031, 3244373, 15904999, 78180131, 385141745, 1900808447, 9395586359, 46502309921, 230413447773, 1142763706389, 5672369968137, 28176421469243, 140049400473211, 696494762630355, 3465512981413485, 17250679866579039, 85903957507564797
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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M. Bouquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
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, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, -1 + j, -1 + n] + aux[-1 + i, j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]
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CROSSREFS
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Sequence in context: A163606 A115968 A005827 this_sequence A151222 A151223 A151224
Adjacent sequences: A151316 A151317 A151318 this_sequence A151320 A151321 A151322
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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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