A150643 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, 0, 1), (0, 1, 0), (0, 1, 1), (1, -1, 1), (1, 1, -1)}.

1, 2, 7, 27, 117, 524, 2426, 11426, 54567, 262976, 1276549, 6229483, 30526069, 150072090, 739706710, 3653663305, 18077660610, 89571457084, 444331922248, 2206345069415, 10964807311084, 54530053703043, 271352454159710, 1351007442499864, 6729414090351049, 33532553606501833, 167149180130979290

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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A175934 A150641 A150642 * A150644 A007166 A036783

Adjacent sequences: A150640 A150641 A150642 * A150644 A150645 A150646

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved