A149304 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, 1), (-1, 1, 1), (1, 0, -1), (1, 0, 1)}.

1, 1, 4, 11, 48, 153, 695, 2461, 11430, 42933, 202241, 790669, 3760536, 15125411, 72443050, 297652719, 1433159704, 5986967421, 28945946323, 122535705935, 594410042334, 2543786121717, 12373361059432, 53434246508299, 260504421338140, 1133661768994795, 5537534006629171, 24257661377551561

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A053882 A246652 A254202 * A149305 A149306 A149307

Adjacent sequences: A149301 A149302 A149303 * A149305 A149306 A149307

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved