A151505 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, -1), (1, 0)}

1, 2, 12, 101, 1032, 11920, 149961, 2009612, 28274682, 413539023, 6242609402, 96747540753, 1533113138015, 24762204978303, 406616430143397, 6774369810238176, 114316146704465162, 1951147377176414045, 33643578373731545756, 585472973069805944673, 10273759638672970806593, 181654478085079820726152

Offset

0,2

Links

Table of n, a(n) for n=0..21.

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, j, -1 + n] + aux[-1 + i, 1 + 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: A055865 A085389 A202013 * A096347 A137483 A113557

Adjacent sequences: A151502 A151503 A151504 * A151506 A151507 A151508

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved