A151357 Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 0), (0, 1), (1, -1), (1, 0)}.

1, 0, 1, 3, 4, 20, 65, 175, 742, 2604, 9072, 36960, 139392, 538824, 2198625, 8735727, 35456850, 146812952, 604215326, 2521642266, 10617725768, 44760668160, 190357768328, 813800295880, 3490232753680, 15055389124320, 65193213272800, 283254330047520, 1235731377864960, 5407996483238160

Offset

0,4

Links

Table of n, a(n) for n=0..29.

M. Bousquet-Mélou and M. Mishna, Walks with small steps in the quarter plane, arXiv:0810.4387 [math.CO], 2008-2009.

Formula

G.f.: Int(Int(2*hypergeom([3/4,5/4],[2],64*t^3*(t+1)/(1-4*t^2)^2)/(1-4*t^2)^(3/2),t),t)/t^2. - Mark van Hoeij, Aug 14 2014

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

Crossrefs

Sequence in context: A151419 A067281 A326424 * A250105 A009169 A265710

Adjacent sequences: A151354 A151355 A151356 * A151358 A151359 A151360

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved