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A148801 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), (1, 0, 1), (1, 1, -1)} 0
1, 1, 3, 8, 26, 78, 271, 896, 3228, 11119, 41002, 145548, 545187, 1974923, 7480699, 27503349, 105050951, 390597492, 1501505042, 5632087999, 21759951598, 82196014521, 318859845293, 1211380162124, 4714855246296, 17997471462958, 70241280052488, 269196555472317, 1053057343103259, 4049528715390724 (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, 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: A343553 A317852 A306485 * A131910 A205775 A331320
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified November 28 08:03 EST 2023. Contains 367394 sequences. (Running on oeis4.)