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Search: id:A151293
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| A151293 |
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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), (1, -1), (1, 1)} |
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+0
1
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| 1, 2, 7, 24, 88, 328, 1246, 4779, 18485, 71918, 281102, 1102653, 4337842, 17104951, 67577658, 267410057, 1059581561, 4203221319, 16689714274, 66324649355, 263761185264, 1049579758069, 4178825351781, 16645543692333, 66331807758634, 264426232745902, 1054454512710944, 4206064951123326
(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, 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: A131824 A150389 A104625 this_sequence A122446 A150390 A052705
Adjacent sequences: A151290 A151291 A151292 this_sequence A151294 A151295 A151296
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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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