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A148075 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, 1, 0), (0, 0, 1), (1, 0, -1)} 0
1, 1, 2, 4, 9, 21, 56, 169, 482, 1505, 4655, 14419, 46683, 153632, 522567, 1760914, 6050077, 20830801, 72215812, 256321026, 908687720, 3272602542, 11754785559, 42458425816, 154767487534, 565357807589, 2092065007291, 7725542715670, 28717905731799, 106970060346082, 399403757982693, 1504067532147492 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..31.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

MATHEMATICA

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, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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}]

CROSSREFS

Sequence in context: A130866 A123458 A048194 * A058718 A148076 A217976

Adjacent sequences:  A148072 A148073 A148074 * A148076 A148077 A148078

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified April 8 04:26 EDT 2020. Contains 333312 sequences. (Running on oeis4.)