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A150276
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), (0, 1, 0), (1, 0, 1)}.
0
1, 2, 6, 23, 88, 352, 1471, 6229, 26846, 117199, 516047, 2293107, 10253796, 46099289, 208317929, 945090949, 4303253468, 19657172870, 90040264031, 413482527121, 1903072433181, 8776676137009, 40552191411904, 187684377800197, 869986408121608, 4038465213131538, 18771067305712298, 87355565476467784
OFFSET
0,2
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, 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: A247211 A150275 A335537 * A189043 A228392 A190910
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified September 19 23:07 EDT 2024. Contains 376015 sequences. (Running on oeis4.)