A150846 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, 0, 0), (1, -1, 0), (1, 0, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 8, 32, 140, 610, 2756, 12514, 57848, 268436, 1257928, 5915546, 27991248, 132843454, 633110652, 3024787472, 14495342620, 69608204042, 335037749148, 1615403739132, 7802947707912, 37746275219340, 182865537439992, 887020568383374, 4307942307676976, 20944703634327626, 101936878569261388

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, 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: A151304 A151828 A150845 * A150847 A150848 A150849

Adjacent sequences: A150843 A150844 A150845 * A150847 A150848 A150849

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved