A151126 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, 0, 0), (1, 0, 1)}.

1, 3, 11, 45, 195, 861, 3883, 17849, 82871, 387677, 1828331, 8675753, 41340895, 197798741, 949965235, 4575464321, 22091621351, 106919166509, 518529548539, 2519023057881, 12257015683439, 59728345794373, 291428334763011, 1423587793003185, 6961613105336055, 34077231356905437, 166956506929848715

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, j, -1 + k, -1 + n] + aux[-1 + i, 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: A151123 A151124 A151125 * A151127 A026375 A151128

Adjacent sequences: A151123 A151124 A151125 * A151127 A151128 A151129

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved