A151506 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, -1), (-1, 1), (0, -1), (1, -1), (1, 0)}

1, 0, 1, 1, 5, 6, 33, 66, 262, 688, 2614, 7630, 28372, 91490, 333166, 1139686, 4172274, 14771196, 54529720, 198319758, 738538816, 2738271072, 10302251312, 38749276416, 147201935416, 560210700982, 2146843198772, 8250106899418, 31870249952754, 123485120302378, 480468887927340, 1874991897193156

Offset

0,5

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

Crossrefs

Sequence in context: A166023 A137762 A177118 * A122008 A248254 A212918

Adjacent sequences: A151503 A151504 A151505 * A151507 A151508 A151509

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved