A150542 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), (0, 1, -1), (0, 1, 1), (1, 0, -1), (1, 1, 0)}.

1, 2, 7, 26, 103, 431, 1855, 8172, 36617, 166316, 763682, 3537557, 16506691, 77503471, 365818093, 1734513028, 8256719514, 39439734441, 188966919172, 907847268968, 4372082095389, 21101141433849, 102040426087208, 494319114044965, 2398510207471090, 11655029385099377, 56711232690554604, 276287353453444549

Offset

0,2

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, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + 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: A150539 A150540 A150541 * A150543 A150544 A345884

Adjacent sequences: A150539 A150540 A150541 * A150543 A150544 A150545

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved