A151004 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), (1, -1, 1), (1, 0, 1), (1, 1, -1), (1, 1, 1)}.

1, 2, 9, 38, 177, 823, 3950, 18980, 92410, 450797, 2213686, 10886910, 53736619, 265556547, 1315191824, 6519528720, 32362495781, 160757651597, 799283898700, 3976159739835, 19792661537235, 98565692978344, 491074245949516, 2447429780696681, 12201725563707248, 60847702887696883, 303514469453973168

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + 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: A151002 A151003 A357547 * A151005 A105484 A151006

Adjacent sequences: A151001 A151002 A151003 * A151005 A151006 A151007

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved