A150127 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, 0), (-1, 0, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 6, 20, 70, 260, 986, 3852, 15284, 61646, 251636, 1038026, 4320900, 18123780, 76544604, 325197844, 1389044326, 5961411840, 25695687106, 111190743966, 482866090476, 2103799954064, 9193627059292, 40287920890732, 177002193428102, 779506763324538, 3440547333117048, 15217327587907986

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, 1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A092413 A151285 A150126 * A151286 A047126 A145138

Adjacent sequences: A150124 A150125 A150126 * A150128 A150129 A150130

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved