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Search: id:A148446
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| A148446 |
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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, 1), (-1, 1, 1), (0, 1, 1), (1, 0, -1)} |
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+0
1
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| 1, 1, 2, 6, 17, 49, 170, 567, 1938, 7048, 25692, 94221, 355939, 1358403, 5196687, 20169943, 79178940, 311341768, 1233884011, 4934811327, 19786170788, 79683695476, 323069731308, 1313959977470, 5358853327284, 21960167792626, 90282256030304, 371942734756058, 1537483777024417, 6374355298767209
(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, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A122099 A026165 A148445 this_sequence A027914 A098703 A025272
Adjacent sequences: A148443 A148444 A148445 this_sequence A148447 A148448 A148449
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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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