A149709 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, 0, 1), (0, -1, 1), (0, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 71, 281, 1207, 5115, 22351, 97707, 433499, 1929001, 8656613, 38971527, 176423283, 800930495, 3650497845, 16678891433, 76432737821, 350991616137, 1615597227275, 7449843874121, 34418117313089, 159257262101047, 738069917061899, 3425157420368435, 15916408813951505, 74049435062799305

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[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A146511 A128887 A149708 * A149710 A149711 A149712

Adjacent sequences: A149706 A149707 A149708 * A149710 A149711 A149712

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved