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A151356
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Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 0), (-1, 1), (0, -1), (1, -1), (1, 1)}
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0
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1, 0, 1, 2, 8, 22, 101, 364, 1618, 6702, 30512, 135904, 634610, 2958340, 14147829, 67996988, 331941976, 1631261090, 8101797506, 40502662220, 204075069854, 1034325813080, 5274800747204, 27039112223056, 139308940725640, 720950926411856, 3747030865713930, 19550315832999732, 102379532471138668
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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LINKS
| M. Bousquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
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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, -1 + j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[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[aux[0, 0, n], {n, 0, 25}]
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CROSSREFS
| Sequence in context: A072929 A053958 A191643 * A158466 A065694 A178129
Adjacent sequences: A151353 A151354 A151355 * A151357 A151358 A151359
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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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