A149740 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, 1), (1, -1, 0), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 77, 307, 1417, 6183, 28931, 130781, 620821, 2872353, 13745911, 64565453, 311110427, 1476837549, 7149499395, 34210853287, 166255385207, 800280846231, 3900765769399, 18866279455493, 92183448334125, 447524609954737, 2191122851174113, 10670204506489859, 52330715761458845, 255485726420231277

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, j, -1 + 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: A149737 A149738 A149739 * A149741 A149742 A149743

Adjacent sequences: A149737 A149738 A149739 * A149741 A149742 A149743

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved