A150528 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), (1, -1, 0), (1, 0, 0), (1, 1, 1)}.

1, 2, 7, 25, 105, 430, 1917, 8344, 38339, 172896, 808947, 3725645, 17647275, 82496002, 394115323, 1862212671, 8953469157, 42647136320, 206057059233, 987669413703, 4790583308431, 23076758351160, 112282290880467, 543068170841868, 2649172135026177, 12855938931981320, 62848396027216011, 305844516598799957

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, j, k, -1 + n] + aux[-1 + i, 1 + j, 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: A150525 A150526 A150527 * A150529 A286761 A150530

Adjacent sequences: A150525 A150526 A150527 * A150529 A150530 A150531

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved