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(-2+Int(6*(1-9*x)*(1-Int(4*(1-2*x-15*x^2)^(3/2)*((1830*x^5+59*x^4+362*x^3+22*x^2-8*x+3)*(1-4*x^2)*hypergeom([7/4, 9/4],[2],64*x^3*(1+x)/(1-4*x^2)^2)+7*(750*x^4-307*x^3-213*x^2-45*x+11) *x^3*hypergeom([9/4, 11/4],[3],64*x^3*(1+x)/(1-4*x^2)^2))/((1-4*x^2)^(9/2)*(9*x-1)^2*(1+x)),x))/(1-2*x-15*x^2)^(5/2),x),x),x)/(x^2*(x-1)). - 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[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
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved