A149205 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, 0), (-1, 0, 0), (-1, 1, -1), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 10, 40, 129, 537, 1933, 8328, 31833, 140729, 559013, 2518826, 10280324, 46991877, 195714236, 904660544, 3827438751, 17850086730, 76473277330, 359252690128, 1554944844436, 7349047127951, 32080478571693, 152395736480523, 670039535488503, 3196878057937120, 14142253394919290

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + 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: A136859 A051479 A149204 * A149206 A149207 A156798

Adjacent sequences: A149202 A149203 A149204 * A149206 A149207 A149208

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved