A151003 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, 0), (0, -1, 1), (0, 1, 1), (1, 1, -1), (1, 1, 1)}.

1, 2, 9, 38, 176, 823, 3923, 18896, 91764, 447969, 2197018, 10808493, 53314066, 263518119, 1304635500, 6467863885, 32100843512, 159468346798, 792819418523, 3944217414510, 19633286243766, 97776890309758, 487148147762393, 2427973454113814, 12104993886409944, 60367867058622098, 301129528117164483

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, -1 + k, -1 + n] + aux[1 + i, 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: A151000 A151001 A151002 * A357547 A151004 A151005

Adjacent sequences: A151000 A151001 A151002 * A151004 A151005 A151006

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved