A149897 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, 0, 1), (0, 1, 0), (1, 0, -1)}.

1, 2, 5, 14, 46, 162, 595, 2261, 8841, 35340, 143811, 594390, 2488519, 10533645, 45014997, 193970548, 841930778, 3678034790, 16160393595, 71371290127, 316672410576, 1410982150790, 6310902015761, 28325384296781, 127540370321842, 575963773128130, 2608068991503519, 11839437921469267

Offset

0,2

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, j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 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: A232622 A149895 A149896 * A124527 A149898 A240611

Adjacent sequences: A149894 A149895 A149896 * A149898 A149899 A149900

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved