A150339 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, 0, -1), (0, 0, 1), (1, 0, 1)}.

1, 2, 7, 23, 86, 324, 1299, 5248, 21803, 91109, 386870, 1652908, 7140192, 31015614, 135755899, 596894225, 2639027048, 11712554874, 52208189271, 233481867841, 1047793276565, 4715377052267, 21281091083730, 96276529269418, 436603412361372, 1984114640043230, 9035173400355720, 41219771952879434

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, 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, -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: A352173 A150337 A150338 * A150340 A339038 A001338

Adjacent sequences: A150336 A150337 A150338 * A150340 A150341 A150342

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved