A149919 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, 0, -1), (0, 1, 0), (1, 0, 0)}.

1, 2, 5, 15, 47, 157, 549, 1982, 7354, 27927, 107979, 424329, 1690034, 6812041, 27739662, 114012290, 472388018, 1971765577, 8284065362, 35014751268, 148798722863, 635518054040, 2726620459966, 11748054498309, 50814320078733, 220590909294021, 960812893101569, 4198183258800311

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, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 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: A149917 A149918 A353028 * A149920 A149921 A149922

Adjacent sequences: A149916 A149917 A149918 * A149920 A149921 A149922

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved