A150375 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), (-1, 0, 0), (1, 0, 1), (1, 1, 0)}.

1, 2, 7, 23, 96, 354, 1534, 6066, 27086, 110747, 501581, 2106197, 9652273, 41197318, 190177775, 823152541, 3823689704, 16712997276, 77975705509, 343795036066, 1610189417951, 7146230164544, 33567668815079, 149865434397075, 705794290614539, 3166119611677456, 14941943012113508, 67320026715907005

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, -1 + k, -1 + n] + aux[1 + i, j, 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: A150373 A150374 A326648 * A150376 A150377 A150378

Adjacent sequences: A150372 A150373 A150374 * A150376 A150377 A150378

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved