A150837 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, 0), (0, 1, 1), (1, 0, -1), (1, 1, 1)}.

1, 2, 8, 32, 137, 603, 2733, 12548, 58366, 273838, 1294196, 6151513, 29378090, 140853763, 677586477, 3268830837, 15808422237, 76615362124, 372015952802, 1809389360612, 8813513314809, 42987851976842, 209925510352170, 1026262594674073, 5022074492804672, 24598133511548824, 120582165717981781

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, -1 + j, -1 + 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] + 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: A150834 A150835 A150836 * A150838 A150839 A150840

Adjacent sequences: A150834 A150835 A150836 * A150838 A150839 A150840

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved