A149145 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, 0), (1, -1, -1), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 9, 36, 116, 452, 1613, 6390, 24192, 98022, 383304, 1568862, 6271646, 25946098, 105492537, 439845324, 1809101840, 7589944482, 31515272858, 132927819060, 556072151042, 2355529776828, 9913350863408, 42150753753288, 178288844129100, 760495077330246, 3230288897150356, 13817292281947918

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[-1 + 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, -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: A149142 A149143 A149144 * A262473 A001256 A372211

Adjacent sequences: A149142 A149143 A149144 * A149146 A149147 A149148

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved