A149634 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, 0), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 15, 69, 229, 1103, 4123, 20063, 78141, 383261, 1547761, 7628147, 31532753, 155942825, 656344887, 3253277131, 13881923067, 68926594631, 297404679961, 1478590735749, 6437969004419, 32038866205609, 140560828355783, 700049236582825, 3091048262962159, 15404168399076947, 68393267785098855

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[1 + i, -1 + j, 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: A079569 A149632 A149633 * A149635 A149636 A149637

Adjacent sequences: A149631 A149632 A149633 * A149635 A149636 A149637

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved