A151424 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of 2 n steps taken from {(-1, -1), (-1, 0), (-1, 1), (1, 0), (1, 1)}.

1, 5, 58, 864, 14532, 262644, 4977800, 97575176, 1961361993, 40200713991, 836868065805, 17643727208475, 375932890593208, 8081825426016234, 175078871453866363, 3818046005021353980, 83747799012137460437, 1846442940744222053799, 40896246043951637989485, 909514786452244849526786

Offset

0,2

Links

Table of n, a(n) for n=0..19.

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, j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[0, k, 2 n], {k, 0, 2 n}], {n, 0, 25}]

Crossrefs

Sequence in context: A334698 A129897 A256218 * A097631 A365013 A130768

Adjacent sequences: A151421 A151422 A151423 * A151425 A151426 A151427

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved