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A148791 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, 0, 0), (0, -1, 1), (0, 1, 1), (1, 0, -1)}. 0
1, 1, 3, 8, 25, 77, 257, 865, 3021, 10549, 37753, 135438, 494280, 1806200, 6678951, 24716159, 92336889, 345207465, 1299979995, 4897841100, 18561069686, 70366144206, 268059657293, 1021470014124, 3908025765480, 14955232173032, 57425244146832, 220542549019640, 849474612586124, 3272448053938140 (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, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A148789 A088327 A148790 * A148792 A007563 A050383
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified March 19 06:47 EDT 2024. Contains 370953 sequences. (Running on oeis4.)