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Search: id:A151090
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| A151090 |
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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, 0), (0, 0, 1), (0, 1, 0), (1, 1, 1)} |
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+0
1
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| 1, 3, 11, 43, 175, 731, 3111, 13427, 58591, 257947, 1143943, 5104419, 22896303, 103169899, 466725143, 2118787187, 9648585791, 44060516667, 201709358631, 925531659971, 4255568177615, 19604179972363, 90468636882231, 418164385032723, 1935725673812575, 8973094439246811, 41648668456569671
(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, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A007583 A026671 A026876 this_sequence A059278 A151091 A151092
Adjacent sequences: A151087 A151088 A151089 this_sequence A151091 A151092 A151093
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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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