A151098 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), (0, 0, -1), (0, 0, 1), (0, 1, 0), (1, 0, 1)}.

1, 3, 11, 43, 180, 779, 3451, 15540, 70890, 326746, 1518313, 7102702, 33411343, 157912141, 749357484, 3568438872, 17044813008, 81634173640, 391911036313, 1885504214950, 9088637547932, 43885500213236, 212239044292038, 1027901835175024, 4984800111721564, 24202918927594738, 117644341861522563

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[i, -1 + j, 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A284720 A151096 A151097 * A277220 A338999 A151099

Adjacent sequences: A151095 A151096 A151097 * A151099 A151100 A151101

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved