A151409 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, 0), (0, 1), (1, -1), (1, 1)}.

1, 1, 2, 5, 14, 39, 116, 364, 1154, 3712, 12245, 40940, 137779, 468927, 1612511, 5576133, 19394557, 67912071, 238967041, 844127643, 2994719855, 10665904225, 38103524211, 136531060288, 490663266986, 1767779916316, 6383507664304, 23102978335829, 83786075774791, 304420859569058, 1108009834275929

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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

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, j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A027035 A102406 A307754 * A339289 A003054 A317553

Adjacent sequences: A151406 A151407 A151408 * A151410 A151411 A151412

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved