OFFSET
0,3
LINKS
M. Bousquet-Mélou and M. Mishna, Walks with small steps in the quarter plane, ArXiv 0810.4387, 2008.
FORMULA
G.f.: ((1-5*x)*Int((hypergeom([1/2,1/2],[1],16*x*(1+x)/ (1+4*x)^2)+8*x*hypergeom([1/2,1/2],[2],16*x*(1+x)/(1+4*x)^2))/((5*x-1)^2*(1+4*x)),x)-x)/(4*x^2). - 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, 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, -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