A149784 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, 1), (0, -1, 1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 19, 81, 349, 1555, 7053, 32497, 151005, 708409, 3344375, 15879317, 75743615, 362725533, 1742819393, 8398499171, 40573677013, 196450014697, 953043821113, 4631611218959, 22543961216383, 109885301062387, 536291022892125, 2620369720961805, 12816847429043339, 62750550805668051, 307494459419443003

Offset

0,3

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, -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, -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: A149781 A149782 A149783 * A240688 A149785 A149786

Adjacent sequences: A149781 A149782 A149783 * A149785 A149786 A149787

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved