A151089 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), (0, 0, 1), (0, 1, -1), (1, 0, 0), (1, 0, 1)}.

1, 3, 11, 42, 173, 741, 3261, 14629, 66672, 307495, 1431450, 6715136, 31703007, 150464688, 717305665, 3432702614, 16481592146, 79360476348, 383088631773, 1853344703925, 8983927819733, 43625245683247, 212174495217113, 1033391264252507, 5039581431368101, 24605471797953916, 120263059399576252

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[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: A149068 A151088 A149069 * A211854 A200212 A149070

Adjacent sequences: A151086 A151087 A151088 * A151090 A151091 A151092

Keyword

nonn,walk,changed

Author

Manuel Kauers, Nov 18 2008

Status

approved