A149474 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, 0, 1), (1, -1, 1), (1, 1, -1), (1, 1, 0)}.

1, 1, 4, 13, 56, 217, 1007, 4323, 20408, 91485, 440772, 2039543, 9903272, 46648424, 228365295, 1090701055, 5361007008, 25835934259, 127498368909, 618915161987, 3061302337978, 14936675176933, 74044185072569, 362807052727618, 1801022351300727, 8852665926284525, 44004117721904990, 216871110702639661

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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A149473 A365854 A188205 * A149475 A149476 A121076

Adjacent sequences: A149471 A149472 A149473 * A149475 A149476 A149477

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved