A148572 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, 1, -1), (1, -1, 1), (1, 0, 0)}.

1, 1, 3, 6, 19, 54, 183, 632, 2307, 8753, 34000, 135893, 552498, 2288861, 9619432, 40955833, 176439889, 767614597, 3370686080, 14919375855, 66519132927, 298537169659, 1347748022530, 6117531357164, 27904394951401, 127858017889598, 588274930715447, 2716966368936216, 12592645826466517

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, j, k, -1 + n] + aux[-1 + 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, 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: A148570 A148571 A345400 * A320174 A248603 A332344

Adjacent sequences: A148569 A148570 A148571 * A148573 A148574 A148575

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved