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A151272
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Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 0), (0, -1), (1, -1), (1, 1)}.
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0
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1, 1, 4, 11, 34, 112, 376, 1257, 4330, 15068, 52570, 185086, 657128, 2339972, 8366910, 30070119, 108400594, 391749772, 1420203840, 5161860950, 18797194292, 68593029228, 250803101058, 918497353314, 3368841454202, 12375002551280, 45518663980004, 167631635849400, 618071950062304, 2281410957097608
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OFFSET
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0,3
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LINKS
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M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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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, j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]
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CROSSREFS
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KEYWORD
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nonn,walk
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AUTHOR
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STATUS
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approved
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