A151485 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), (-1, 1), (0, -1), (0, 1), (1, 0), (1, 1)}.

1, 1, 6, 20, 95, 432, 2100, 10429, 52990, 273872, 1435464, 7610704, 40747432, 219972284, 1196042952, 6543872976, 36000272857, 199016494848, 1104987607068, 6159118520824, 34451516940832, 193323839813568, 1087995843781768, 6139413903894528, 34728866786674200, 196895381265884724

Offset

0,3

Links

Table of n, a(n) for n=0..25.

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

Formula

G.f.: 1+6*Int(Int(Int(x*(14+Int((1-4*x-12*x^2)^(3/2)*((-160*x^4-176*x^3-56*x^2-8*x-1)*hypergeom([5/4, 7/4],[1],64*x^3*(2*x+1)/(8*x^2-1)^2)+4*x^2*(32*x^3-10*x^2-19*x-4)*hypergeom([5/4, 7/4],[2], 64*x^3*(2*x+1)/(8*x^2-1)^2))/((2*x+1)*(1-8*x^2)^(7/2)*x^2),x))/(1-4*x-12*x^2)^(5/2),x),x),x)/x^2. - Mark van Hoeij, Aug 27 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, -1 + j, -1 + n] + aux[-1 + i, j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + 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: A226638 A274071 A246036 * A191424 A333048 A200538

Adjacent sequences: A151482 A151483 A151484 * A151486 A151487 A151488

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved