A150545 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, 0, 1), (0, 1, -1), (0, 1, 1), (1, 0, 1)}.

1, 2, 7, 26, 104, 424, 1799, 7702, 33516, 147394, 652986, 2914743, 13083333, 58999874, 267246535, 1214730328, 5539131519, 25330977489, 116127158302, 533596390917, 2456884051208, 11333435962029, 52370456329081, 242376654647296, 1123371423517327, 5213627047990241, 24226805860447941, 112708523641261090

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[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A150543 A150544 A345884 * A150546 A151296 A141370

Adjacent sequences: A150542 A150543 A150544 * A150546 A150547 A150548

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved