A151407 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, 0), (1, 1)}.

1, 0, 2, 2, 8, 21, 56, 180, 537, 1642, 5428, 16894, 56073, 184644, 608722, 2060761, 6912591, 23511436, 80469490, 275394728, 951992172, 3293896039, 11446970617, 39969401778, 139770090303, 490850856487, 1727806323657, 6096204817107, 21572269339099, 76472370379535, 271723970484170, 967416967381241

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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[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: A167532 A208235 A151377 * A377243 A130102 A151384

Adjacent sequences: A151404 A151405 A151406 * A151408 A151409 A151410

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved