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Search: id:A148093
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| A148093 |
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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, 0), (0, -1, 1), (0, 1, 0), (1, 0, -1)} |
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+0
1
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| 1, 1, 2, 4, 10, 25, 70, 212, 639, 2000, 6451, 21617, 71791, 246306, 858806, 3031680, 10707284, 38611784, 140802398, 514700655, 1893610027, 7056144208, 26475930759, 99365898413, 375942742181, 1434074803915, 5489981644607, 21037233338679, 81212735932262, 315232763329880, 1225469410310123, 4774478236859757
(list; graph; listen)
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OFFSET
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0,3
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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, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A052829 A001998 A005817 this_sequence A148094 A148095 A124419
Adjacent sequences: A148090 A148091 A148092 this_sequence A148094 A148095 A148096
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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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