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A151133 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), (0, 0, 1), (0, 1, 0), (1, 0, 1), (1, 1, -1)} 0
1, 3, 11, 45, 199, 907, 4230, 20033, 95911, 462904, 2247962, 10968589, 53721197, 263906906, 1299630087, 6413037954, 31698197261, 156896920042, 777515340136, 3856929118269, 19149163595612, 95144059740028, 473036014994715, 2353159229072661, 11711770890571388, 58315249692444070, 290474484967129825 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[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: A151132 A200075 A187764 * A213333 A083886 A030866
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified April 13 04:33 EDT 2024. Contains 371639 sequences. (Running on oeis4.)