A151304 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 1), (-1, 0), (0, 1), (1, -1), (1, 1)}

1, 2, 8, 32, 139, 612, 2780, 12777, 59474, 279119, 1319587, 6272549, 29957777, 143629361, 690899877, 3332790064, 16116297361, 78099554494, 379183671290, 1844059563096, 8981468647748, 43802659925084, 213883830813678, 1045516504740462, 5115841042217242, 25055289097485312, 122813356787701498

Offset

0,2

Links

Table of n, a(n) for n=0..26.

M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, -1 + j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A150843 A150844 A141380 * A151828 A150845 A150846

Adjacent sequences: A151301 A151302 A151303 * A151305 A151306 A151307

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved