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Search: id:A149853
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| A149853 |
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Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, -1), (-1, 0, 1), (0, 1, 0), (1, 0, 0)} |
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+0
1
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| 1, 2, 5, 13, 35, 104, 318, 1014, 3256, 10543, 34937, 116848, 397242, 1354804, 4641335, 16053619, 55784113, 195466771, 686258063, 2416219435, 8551265471, 30349165784, 108247450688, 386615499598, 1383536609787, 4967118466568, 17866856266359, 64477119071662, 232917119736270, 842589117795023, 3054850488851820
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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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, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
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CROSSREFS
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Sequence in context: A131868 A000747 A151259 this_sequence A148291 A148292 A148293
Adjacent sequences: A149850 A149851 A149852 this_sequence A149854 A149855 A149856
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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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