A150073 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, -1, 1), (0, 0, 1), (0, 1, -1), (1, 0, 1)}.

1, 2, 6, 18, 65, 240, 918, 3609, 14571, 59624, 247322, 1038351, 4401989, 18803632, 80903679, 350281242, 1524630402, 6667663326, 29286656081, 129132109006, 571345532548, 2535959521772, 11288724438289, 50384304361736, 225426802809994, 1010875691689569, 4542536427012601, 20452372960668591

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, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A007454 A305578 A150072 * A150074 A349367 A300335

Adjacent sequences: A150070 A150071 A150072 * A150074 A150075 A150076

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved