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A150168 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), (0, 1, 0), (1, 0, -1), (1, 1, 0)}. 0
1, 2, 6, 20, 75, 297, 1223, 5178, 22441, 98884, 442283, 2000916, 9142251, 42116199, 195395624, 912044028, 4279777216, 20176137436, 95507078481, 453744740526, 2162709310394, 10338309423180, 49549707152860, 238047836414608, 1146105257197884, 5528901726159039, 26719869652877299, 129343971140839144 (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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[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: A148483 A150166 A150167 * A145870 A134957 A052889
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified June 15 06:51 EDT 2024. Contains 373402 sequences. (Running on oeis4.)