A149174 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, 0), (-1, 0, 0), (-1, 1, -1), (0, -1, 1), (1, 1, 0)}.

1, 1, 4, 10, 34, 118, 411, 1538, 5769, 22118, 86604, 340926, 1363754, 5487497, 22284031, 91060167, 374275887, 1546749984, 6419406754, 26758916234, 111933134273, 469802568778, 1977772435371, 8348323510282, 35328472561762, 149837566877982, 636847860037219, 2711964381561554, 11569269389329031

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + 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: A182645 A006343 A149173 * A283070 A222631 A030003

Adjacent sequences: A149171 A149172 A149173 * A149175 A149176 A149177

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved