A150297 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, 0), (-1, 1, 1), (0, 1, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 6, 23, 96, 412, 1819, 8165, 37244, 172041, 802068, 3766707, 17797247, 84512353, 403062511, 1929377961, 9264898815, 44613567669, 215353482998, 1041777792180, 5049322884229, 24515402802290, 119211717497632, 580509003433142, 2830439159149030, 13816713360019538, 67517940619384443

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A150296 A134064 A111283 * A150298 A280768 A370183

Adjacent sequences: A150294 A150295 A150296 * A150298 A150299 A150300

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved