A149427 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), (1, -1, 0), (1, 0, -1), (1, 1, 1)}

1, 1, 4, 13, 44, 150, 548, 1979, 7324, 27074, 101620, 381338, 1444860, 5478476, 20902380, 79824913, 306175148, 1175699494, 4528970884, 17465198198, 67512268620, 261240684772, 1012744843508, 3929870352586, 15272109227396, 59401882159868, 231326540050700, 901564182638872, 3517261162906916

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[-1 + i, 1 + j, 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: A027127 A326329 A073717 * A290907 A252933 A229397

Adjacent sequences: A149424 A149425 A149426 * A149428 A149429 A149430

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved