A148450 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, 1, 0), (-1, 1, 1), (0, 1, 1), (1, 0, -1)}.

1, 1, 2, 6, 17, 50, 171, 569, 1990, 7154, 26001, 96687, 363451, 1383819, 5329430, 20678799, 81004721, 319442630, 1267842963, 5062978205, 20322019887, 81973348695, 332106710789, 1351023998487, 5516694723183, 22603829865743, 92917350331992, 383091765219596, 1583855267724917, 6565396525320192

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A148447 A148448 A148449 * A153773 A059398 A157002

Adjacent sequences: A148447 A148448 A148449 * A148451 A148452 A148453

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved