A149072 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, 1, 1), (0, 1, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 3, 11, 43, 179, 781, 3471, 15741, 72367, 336461, 1577173, 7446583, 35355517, 168668857, 807863711, 3882620245, 18714490787, 90434837781, 437982274021, 2125332358191, 10331177307429, 50297266238485, 245211647137771, 1196962916588179, 5849407909527251, 28614772630350577, 140112559515502989

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[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A219262 A196151 A149071 * A284720 A151096 A151097

Adjacent sequences: A149069 A149070 A149071 * A149073 A149074 A149075

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved