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Search: id:A151453
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| A151453 |
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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 2 n steps taken from {(-1, 0), (-1, 1), (1, -1), (1, 0), (1, 1)} |
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+0
1
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| 1, 4, 42, 578, 9166, 158242, 2891042, 54993704, 1078134132, 21636311154, 442364872960, 9182624116200, 193028135699066, 4100926056901840, 87917821096174026, 1899625977112716534, 41325695763293346504, 904431694783758568086, 19899310516710760870766, 439903811117457581870242
(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.
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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, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[0, k, 2 n], {k, 0, 2 n}], {n, 0, 25}]
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CROSSREFS
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Adjacent sequences: A151450 A151451 A151452 this_sequence A151454 A151455 A151456
Sequence in context: A085954 A046719 A092800 this_sequence A137645 A136045 A074768
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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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