A149845 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, -1, 1), (0, 1, -1), (0, 1, 0), (1, 0, 0)}.

1, 2, 4, 12, 38, 114, 400, 1449, 5046, 19172, 74305, 279604, 1113750, 4496546, 17740654, 72906831, 302544900, 1232387061, 5177998210, 21916697255, 91351341100, 390218601347, 1676532979278, 7110199280273, 30763793677041, 133728879288601, 574879647533236, 2512912116732564, 11026835136668849

Offset

0,2

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, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A139627 A361720 A149844 * A217616 A149846 A341240

Adjacent sequences: A149842 A149843 A149844 * A149846 A149847 A149848

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved