A148854 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, 0, 1), (1, 0, -1), (1, 1, -1)}.

1, 1, 3, 8, 28, 91, 353, 1313, 5279, 21233, 87974, 369069, 1572716, 6763787, 29462557, 129147912, 571417218, 2543626341, 11393262275, 51321889995, 232283468959, 1056120669869, 4821911290022, 22095113714613, 101606770406224, 468712264973306, 2168546809906870, 10060820614451701, 46793794711248079

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 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: A148851 A148852 A148853 * A148855 A148856 A151482

Adjacent sequences: A148851 A148852 A148853 * A148855 A148856 A148857

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved