A148788 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), (-1, 0, 0), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 8, 25, 72, 247, 801, 2790, 9275, 33417, 116063, 421415, 1481888, 5475112, 19691593, 73098992, 264873884, 993746300, 3650365583, 13739262338, 50721769977, 192273730672, 716347593301, 2721804119611, 10176955599081, 38866677109543, 146278605785938, 559635720503905, 2111939759074536

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[1 + i, j, 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: A259700 A213439 A006177 * A292778 A022553 A292884

Adjacent sequences: A148785 A148786 A148787 * A148789 A148790 A148791

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved