OFFSET
0,3
LINKS
M. Bousquet-Mélou and M. Mishna, Walks with small steps in the quarter plane, ArXiv 0810.4387 [math.CO], 2008.
FORMULA
G.f.: Int(Int(Int(x*(-36-2*Int((1-4*x-12*x^2)^(3/2)*((256*x^5+416*x^4+128*x^3+3*x+3)*hypergeom([5/4, 7/4],[1],64*x^3*(2*x+1)/(8*x^2-1)^2)-7*x*(40*x^4+68*x^3-4*x^2-18*x-3)*hypergeom([5/4, 11/4],[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^3. - 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, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[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[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved