A149666 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, -1, 1), (0, 1, -1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 61, 249, 1029, 4393, 18877, 82593, 368597, 1642809, 7460525, 33873153, 155405773, 716194809, 3311534229, 15417851985, 71875081357, 336818380025, 1582087326493, 7450532022801, 35207756508325, 166595086033945, 790683390189869, 3758403182904137, 17898811140511453, 85412862267960161

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, j, 1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A149663 A149664 A149665 * A273327 A273836 A273704

Adjacent sequences: A149663 A149664 A149665 * A149667 A149668 A149669

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved