A150674 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, 0, -1), (0, 0, 1), (0, 1, 1), (1, 1, -1)}.

1, 2, 8, 26, 108, 416, 1772, 7408, 32280, 140864, 626416, 2802480, 12671872, 57632544, 264001184, 1215240512, 5623292864, 26126758656, 121874499712, 570451075712, 2678564077440, 12613073707520, 59549260962304, 281818028251392, 1336656436592128, 6352603760399872, 30248439877778944, 144282137961027584

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[i, -1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 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: A110156 A295934 A187151 * A150675 A150676 A150677

Adjacent sequences: A150671 A150672 A150673 * A150675 A150676 A150677

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved