A149625 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, 1, -1), (1, -1, 0), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 15, 67, 245, 1133, 4649, 21837, 94019, 446511, 1985665, 9507117, 43229887, 208191147, 961692903, 4652119203, 21745052861, 105563020121, 497971021413, 2424374066045, 11519846583297, 56217177871777, 268699372489945, 1313867187813781, 6310262972615505, 30907720460139209, 149043710679987423

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, -1 + j, 1 + k, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A247281 A149623 A149624 * A149626 A149627 A149628

Adjacent sequences: A149622 A149623 A149624 * A149626 A149627 A149628

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved