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Search: id:A151407
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| A151407 |
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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, 0), (1, 1)} |
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+0
1
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| 1, 0, 2, 2, 8, 21, 56, 180, 537, 1642, 5428, 16894, 56073, 184644, 608722, 2060761, 6912591, 23511436, 80469490, 275394728, 951992172, 3293896039, 11446970617, 39969401778, 139770090303, 490850856487, 1727806323657, 6096204817107, 21572269339099, 76472370379535, 271723970484170, 967416967381241
(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, 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: A060823 A167532 A151377 this_sequence A130102 A151384 A113464
Adjacent sequences: A151404 A151405 A151406 this_sequence A151408 A151409 A151410
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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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