A150023 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, 1), (1, -1, 0), (1, 0, 0)}.

1, 2, 5, 18, 67, 258, 1054, 4397, 18726, 81161, 357501, 1591280, 7141591, 32375055, 147738932, 677987483, 3129540083, 14517637716, 67614550769, 316096156970, 1483236166858, 6980705178775, 32943969161726, 155892741042358, 739453402716752, 3514857540660917, 16741114397897829, 79889936502475096

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + 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: A144721 A150021 A150022 * A150024 A150025 A308241

Adjacent sequences: A150020 A150021 A150022 * A150024 A150025 A150026

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved