A149825 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, 0), (-1, 0, 0), (0, 0, 1), (0, 1, 0), (1, -1, -1)}.

1, 2, 4, 10, 28, 85, 275, 910, 3091, 10837, 38949, 142254, 526138, 1971964, 7491686, 28773491, 111407278, 434643804, 1709385164, 6772781723, 26994738921, 108149870681, 435557791070, 1763296481670, 7170999317794, 29276232512536, 119968051032055, 493463560033734, 2036939467083106

Offset

0,2

Links

Table of n, a(n) for n=0..28.

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[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + 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: A289709 A192574 A135336 * A149826 A149827 A149828

Adjacent sequences: A149822 A149823 A149824 * A149826 A149827 A149828

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved