A150912 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, 1, -1), (1, -1, 0), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 31, 147, 600, 2912, 12774, 62607, 285326, 1406716, 6562785, 32476435, 153891360, 763425348, 3657237743, 18174467649, 87764324143, 436691863394, 2121534366438, 10566152542105, 51572492626052, 257038374392677, 1259213728762600, 6279465980796921, 30853842540908054, 153930544834890128

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, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A150909 A150910 A150911 * A165653 A182265 A212873

Adjacent sequences: A150909 A150910 A150911 * A150913 A150914 A150915

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved