A150307 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, 0), (-1, 1, -1), (1, 0, 0), (1, 0, 1)}.

1, 2, 7, 21, 83, 287, 1220, 4555, 20190, 78993, 359409, 1451062, 6720199, 27751565, 130164832, 546754411, 2588819975, 11019871896, 52557679338, 226126679991, 1084651213681, 4707823016596, 22685539977351, 99191227846860, 479765440775025, 2110911015785133, 10241763997702972, 45306172200689549

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A150304 A150305 A150306 * A321283 A150308 A150309

Adjacent sequences: A150304 A150305 A150306 * A150308 A150309 A150310

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved