A150760 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), (0, 1, -1), (1, 0, -1), (1, 1, 0), (1, 1, 1)}

1, 2, 8, 30, 120, 504, 2126, 9202, 40108, 176926, 785348, 3510484, 15771956, 71179114, 322554724, 1466458866, 6688563260, 30585834766, 140219147104, 644209243192, 2965723233464, 13678045731130, 63189872634240, 292379024524178, 1354763058575104, 6285822696135134, 29200842639029914, 135810625365603056

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[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: A133915 A370539 A150759 * A230588 A151303 A150761

Adjacent sequences: A150757 A150758 A150759 * A150761 A150762 A150763

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved