A148304 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, 0, 1), (0, 1, 0), (1, -1, 0), (1, 0, -1)}.

1, 1, 2, 5, 13, 38, 122, 397, 1376, 4923, 17982, 67758, 259896, 1013405, 4024745, 16169249, 65806673, 270873731, 1125025971, 4717447790, 19937273837, 84872224410, 363857572296, 1569265597535, 6807643658516, 29690975231140, 130122867528065, 572952460632662, 2533547362638385

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A369729 A149858 A148303 * A149859 A000800 A149860

Adjacent sequences: A148301 A148302 A148303 * A148305 A148306 A148307

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved