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Search: id:A150078
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| A150078 |
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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, 1, 1), (1, 0, 1), (1, 1, 0)} |
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+0
1
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| 1, 2, 6, 18, 68, 224, 866, 3044, 11856, 42830, 168438, 619340, 2452088, 9130458, 36233300, 136303418, 541799748, 2052445408, 8171539956, 31128440400, 124091086076, 474862499816, 1894225928704, 7277083362774, 29042937826756, 111923855247554, 446900167922820, 1726852464248602
(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, -1 + j, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A057693 A053496 A079577 this_sequence A150079 A150080 A150081
Adjacent sequences: A150075 A150076 A150077 this_sequence A150079 A150080 A150081
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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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