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A148948 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, 1), (0, 0, -1), (1, 0, -1), (1, 1, 0)} 0
1, 1, 3, 9, 30, 102, 395, 1484, 5924, 23995, 98866, 414472, 1762159, 7556734, 32822931, 143522044, 632885962, 2810022936, 12548457073, 56363964503, 254407136619, 1153474144543, 5252345607822, 24004848475242, 110104801267601, 506661531557914, 2338453051900202, 10823603756292646, 50226963438888453 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..28.

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, -1 + j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 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: A304823 A317875 A056333 * A148949 A148950 A148951

Adjacent sequences:  A148945 A148946 A148947 * A148949 A148950 A148951

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified November 14 22:17 EST 2019. Contains 329134 sequences. (Running on oeis4.)