OFFSET
0,2
LINKS
M. Bousquet-Mélou and M. Mishna, Walks with small steps in the quarter plane, ArXiv 0810.4387, 2008.
MAPLE
G := Int(Int((2*(1-8*t^2)*hypergeom([3/4, 5/4], [1], 64*t^2*(t^2+1)/(16*t^2+1)^2)
+12*t^2*hypergeom([3/4, 5/4], [2], 64*t^2*(t^2+1)/(16*t^2+1)^2))/(16*t^2+1)^(5/2), t), t)/t^2;
ogf := subs(t=x^(1/2), series(G, t=0, 40)); # Mark van Hoeij, Aug 20 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, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[0, k, 2 n], {k, 0, 2 n}], {n, 0, 25}]
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved