A150562 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), (0, 1, 1), (1, 0, 1)}.

1, 2, 7, 26, 107, 435, 1864, 8017, 35094, 154374, 687651, 3070614, 13814330, 62358004, 282812259, 1285949237, 5868965797, 26844046407, 123111756347, 565732128917, 2605268895704, 12017396102369, 55531436300662, 256979255171808, 1190949754852390, 5526397573752574, 25676683605056729, 119431826709507381

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, -1 + k, -1 + n] + aux[i, -1 + j, -1 + 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: A150560 A150561 A122871 * A150563 A150564 A150565

Adjacent sequences: A150559 A150560 A150561 * A150563 A150564 A150565

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved