OFFSET
0,2
LINKS
M. Bousquet-Mélou and M. Mishna, Walks with small steps in the quarter plane, arXiv:0810.4387 [math.CO], 2008-2009.
FORMULA
G.f.: Int(hypergeom([1/2,3/2],[2],16*x/(1+4*x))/(1+4*x)^(1/2),x)/x. - Mark van Hoeij, Aug 20 2014
a(n) = (-1)^n*(1+n/3)*binomial(2*n+1,n)*hypergeom([5/2,-n],[4],4)/(2*n+1) = A000108(n)*(A001006(n)+A001006(n+1))*(n+3)/6. - Mark van Hoeij, Aug 24 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[1 + i, 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