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Search: id:A151271
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| A151271 |
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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, -1), (-1, 0), (1, -1), (1, 1)} |
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+0
1
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| 1, 1, 4, 9, 32, 92, 324, 1013, 3612, 11790, 42448, 142522, 516780, 1769552, 6452240, 22416043, 82098940, 288430178, 1060206808, 3757982994, 13855171352, 49467576888, 182845418208, 656756066722, 2432861173012, 8782954641748, 32597120211472, 118191603519288, 439389746023616, 1599141417261936
(list; graph; listen)
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OFFSET
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0,3
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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, 1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + 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: A071378 A053192 A005985 this_sequence A149115 A149116 A149117
Adjacent sequences: A151268 A151269 A151270 this_sequence A151272 A151273 A151274
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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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