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Search: id:A151437
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| A151437 |
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Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, -1), (-1, 1), (0, -1), (1, -1), (1, 1)} |
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+0
1
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| 1, 0, 2, 2, 14, 28, 148, 408, 1948, 6316, 29164, 103336, 473860, 1770364, 8141872, 31491484, 145696432, 577601620, 2689508560, 10864037780, 50889023352, 208655144644, 982532205120, 4078460733332, 19292955235136, 80919972951468, 384307594445168, 1626307851201068, 7750396627918568
(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.
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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, -1 + j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]
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CROSSREFS
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Sequence in context: A032134 A032038 A151353 this_sequence A166114 A009773 A006929
Adjacent sequences: A151434 A151435 A151436 this_sequence A151438 A151439 A151440
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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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