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A151279
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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), (0, 1), (1, 0)}
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0
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1, 2, 5, 15, 45, 143, 467, 1542, 5209, 17747, 61092, 212350, 742252, 2612743, 9243761, 32849712, 117260065, 420007621, 1509519796, 5441576335, 19667601165, 71265365948, 258803411203, 941809569454, 3433951762933, 12542546602374, 45887701715157, 168139500014093, 616966734043059, 2266918422017956
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| M. Bousquet-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
| 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, j, -1 + n] + aux[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
| Sequence in context: A148353 A071727 A148354 * A149907 A148355 A148356
Adjacent sequences: A151276 A151277 A151278 * A151280 A151281 A151282
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KEYWORD
| nonn,walk
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AUTHOR
| Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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