A149641 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), (-1, 0, 0), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 15, 71, 235, 1147, 4261, 20885, 81049, 399677, 1609593, 7961105, 32824569, 162734865, 683496555, 3394132835, 14457881135, 71884823559, 309701765151, 1541308824347, 6702318246579, 33380693562987, 146283366386803, 728994078707843, 3215695886993247, 16032946387905691, 71123532628247839

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[-1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A355603 A355507 A259205 * A149642 A149643 A149644

Adjacent sequences: A149638 A149639 A149640 * A149642 A149643 A149644

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved