A149373 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, 1), (0, -1, 1), (0, 1, -1), (1, 1, 0)}.

1, 1, 4, 12, 46, 174, 703, 2888, 12148, 51924, 224551, 982451, 4331352, 19247666, 86027816, 386632310, 1745493623, 7912474214, 35995573003, 164273095721, 751821506551, 3449621370468, 15864629611684, 73113526659709, 337594692984764, 1561539606796564, 7234504448723448, 33566690644670128

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[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A149371 A149372 A126202 * A259203 A151464 A101225

Adjacent sequences: A149370 A149371 A149372 * A149374 A149375 A149376

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved