A149572 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), (-1, 1, -1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 13, 63, 203, 999, 3587, 17759, 67651, 336021, 1331219, 6625527, 26986373, 134486323, 559145055, 2788924975, 11780888151, 58797042195, 251528398701, 1255897609137, 5428250453879, 27112257364177, 118192158415853, 590469598600839, 2592741636999165, 12955252325160873, 57239205344554295

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[1 + 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: A149569 A149570 A149571 * A149573 A149574 A301634

Adjacent sequences: A149569 A149570 A149571 * A149573 A149574 A149575

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved