A150276 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, 0, 0), (0, 1, -1), (0, 1, 0), (1, 0, 1)}.

1, 2, 6, 23, 88, 352, 1471, 6229, 26846, 117199, 516047, 2293107, 10253796, 46099289, 208317929, 945090949, 4303253468, 19657172870, 90040264031, 413482527121, 1903072433181, 8776676137009, 40552191411904, 187684377800197, 869986408121608, 4038465213131538, 18771067305712298, 87355565476467784

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, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A247211 A150275 A335537 * A189043 A228392 A190910

Adjacent sequences: A150273 A150274 A150275 * A150277 A150278 A150279

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved