A150098 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, 1), (0, 0, 1), (0, 1, -1), (1, 0, 0)}.

1, 2, 6, 19, 67, 249, 964, 3850, 15727, 65470, 276659, 1183644, 5117229, 22318698, 98081642, 433863665, 1930189533, 8630458362, 38761928782, 174784980244, 790957057597, 3590859857448, 16349677462846, 74639892420144, 341573289801870, 1566608313475864, 7199847839030811, 33151568052565316

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A150096 A150097 A145847 * A184018 A148470 A148471

Adjacent sequences: A150095 A150096 A150097 * A150099 A150100 A150101

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved