A149370 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), (0, 0, -1), (1, -1, 0), (1, 1, 0)}.

1, 1, 4, 12, 46, 160, 643, 2575, 10729, 44624, 190291, 823169, 3608545, 15902256, 70658022, 316491884, 1428784897, 6481876262, 29534326134, 135186987516, 621730458462, 2870676877668, 13296405107770, 61766333479830, 287795260731617, 1344834924402010, 6300001869005030, 29577249454624618

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, k, -1 + n] + aux[i, 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: A006735 A166115 A027288 * A149371 A149372 A126202

Adjacent sequences: A149367 A149368 A149369 * A149371 A149372 A149373

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved