A149014 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), (0, 1, 1), (1, 0, -1), (1, 1, -1)}.

1, 1, 3, 9, 35, 116, 500, 1862, 8294, 33249, 151183, 634813, 2931946, 12703620, 59376538, 263224140, 1241544311, 5601006741, 26605292985, 121687147307, 581285094579, 2688189609858, 12900275303951, 60197931997810, 289988678907296, 1363334026137031, 6588771922311268, 31170328189487342

Offset

0,3

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, 1 + k, -1 + n] + aux[i, -1 + j, -1 + 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: A332370 A130491 A149013 * A149015 A151452 A149016

Adjacent sequences: A149011 A149012 A149013 * A149015 A149016 A149017

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved