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Search: id:A151022
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| A151022 |
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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, 0), (-1, 1, 0), (1, -1, 0), (1, 1, 0), (1, 1, 1)} |
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+0
1
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| 1, 2, 10, 36, 180, 752, 3760, 16736, 83680, 385344, 1926720, 9058512, 45292560, 215891600, 1079458000, 5195196624, 25975983120, 125901336112, 629506680560, 3067403607504, 15337018037520, 75041661844720, 375208309223600, 1841832138224720, 9209160691123600, 45324878456036464, 226624392280182320
(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[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, 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: A026546 A151020 A151021 this_sequence A144895 A154323 A073110
Adjacent sequences: A151019 A151020 A151021 this_sequence A151023 A151024 A151025
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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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