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A151375
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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), (0, 1), (1, -1)}.
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1
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1, 1, 1, 1, 3, 6, 10, 15, 49, 112, 216, 375, 1265, 3069, 6357, 11921, 40845, 102528, 221680, 436203, 1507593, 3869027, 8609811, 17511879, 60844223, 158598846, 360334950, 750899305, 2617859439, 6903200862, 15932387546, 33824479875, 118192674861, 314468570516, 734790352692, 1583113929243, 5540670299185
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..300
M. Bousquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
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MAPLE
| b:= proc(n, x, y) option remember; `if` (n<0 or x<0 or y<0 or n<x, 0, `if` (n=0, `if` (x=0, 1, 0), add (b(n-1, x+d[1], y+d[2]), d=[[-1, -1], [0, 1], [1, -1]]))) end: a:= n-> b(n, 0, 0):
seq (a(n), n=0..50); # Alois P. Heinz, Jul 02 2011
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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[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
| Sequence in context: A058576 A130200 A202269 * A153453 A025215 A049697
Adjacent sequences: A151372 A151373 A151374 * A151376 A151377 A151378
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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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