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A151434
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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), (-1, 1), (0, -1), (0, 1), (1, -1)}
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0
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1, 1, 2, 4, 12, 30, 100, 285, 1018, 3142, 11736, 38276, 147552, 501072, 1977608, 6926828, 27842000, 99938263, 407596014, 1492448436, 6159941412, 22930113936, 95587448784, 360799985580, 1516761327208, 5793529219084, 24531896869176, 94672009465506, 403396322741868, 1570813436684425, 6730083531676042
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..30.
M. Bousquet-Mélou 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[i, -1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + 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
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Sequence in context: A148188 A148189 A148190 * A296292 A287966 A148191
Adjacent sequences: A151431 A151432 A151433 * A151435 A151436 A151437
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers, Nov 18 2008
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STATUS
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approved
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