A150441 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, 0, -1), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 24, 101, 403, 1799, 7729, 35582, 159249, 746868, 3429129, 16279415, 76038150, 364074308, 1721288236, 8293384763, 39561489590, 191523249524, 919823257090, 4469670849133, 21579820508491, 105176803076095, 509931061050852, 2491421983809786, 12120212553997146, 59337609677325128, 289468570292570530

Offset

0,2

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, k, -1 + n] + aux[-1 + i, j, k, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A326336 A150439 A150440 * A150442 A352906 A150443

Adjacent sequences: A150438 A150439 A150440 * A150442 A150443 A150444

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved