A150659 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, 1, 1), (0, 1, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 28, 122, 534, 2444, 11220, 52536, 246840, 1172104, 5580649, 26741260, 128421666, 619275234, 2991804319, 14494707351, 70332745402, 341974970533, 1664926463193, 8118358471204, 39629464167851, 193684934880890, 947500660895119, 4639699212194171, 22737806937630413, 111522036284003882

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -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: A276852 A352861 A293266 * A150660 A150661 A269228

Adjacent sequences: A150656 A150657 A150658 * A150660 A150661 A150662

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved