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Search: id:A151408
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| A151408 |
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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, 0), (0, 1), (1, -1), (1, 0)} |
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+0
1
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| 1, 1, 2, 5, 12, 34, 97, 287, 887, 2761, 8833, 28635, 93897, 312257, 1046368, 3539825, 12066283, 41387197, 142887038, 495828190, 1729130445, 6057385620, 21303526484, 75209346309, 266413953357, 946691896721, 3373935569795, 12056675023892, 43193395482458, 155104308523072, 558187652361721, 2012940278579932
(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, 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[0, k, n], {k, 0, n}], {n, 0, 25}]
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CROSSREFS
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Sequence in context: A004114 A076864 A032292 this_sequence A121956 A131467 A000103
Adjacent sequences: A151405 A151406 A151407 this_sequence A151409 A151410 A151411
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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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