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A149742 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), (1, 1, -1), (1, 1, 1)}. 0
1, 1, 5, 17, 77, 317, 1415, 6333, 28813, 132839, 617129, 2888359, 13611893, 64397119, 306277069, 1461111375, 6994321849, 33574979779, 161548792499, 779091251847, 3764306063501, 18220098464389, 88329628435305, 428817322760587, 2084563208540983, 10145404537779319, 49431229586400457, 241086367397001421 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + 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}]
CROSSREFS
Sequence in context: A149739 A149740 A149741 * A149743 A323794 A151479
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified April 21 22:54 EDT 2024. Contains 371886 sequences. (Running on oeis4.)