A150737 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, 0), (0, 1, -1), (1, 0, 1), (1, 1, 1)}

1, 2, 8, 29, 122, 516, 2253, 10019, 45223, 205633, 948552, 4383695, 20467864, 95853451, 451175590, 2133028680, 10110239852, 48104263016, 229403087222, 1096730547084, 5255720495831, 25229713743029, 121361215731913, 584670220548122, 2821064568974016, 13631559528851392, 65948796453391527

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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A150734 A150735 A150736 * A150738 A150739 A151301

Adjacent sequences: A150734 A150735 A150736 * A150738 A150739 A150740

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved