%I #10 Nov 30 2015 14:49:46
%S 1,1,1,1,3,1,1,4,5,1,1,5,12,7,1,1,6,17,24,9,1,1,7,23,53,40,11,1,1,8,
%T 30,76,117,60,13,1,1,9,38,106,246,217,84,15,1,1,10,47,144,352,580,361,
%U 112,17,1,1,11,57,191,496,1178,1158,557,144,19,1,1,12,68,248,687,1674,2916,2076,813,180,21,1,1,13,80,316,935,2361,5768,6150,3446,1137,220,23,1,1,14,93
%N Square array A(n,k) for n,k>=0, where A(n,k) is the number of paths from (0,0) to (n,k) in the directed graph with vertices (i,j) and edges (i,j)-to-(i+1,j), (i,j)-to-(i,j+1), and (i,i+h)-to-(i+1,i+h+1) for every i,j,h>=0.
%F For n>=2*k, A(n,k) = coefficient of x^k in F(x)*C(x)^(n-2*k). For n<=2*k, A(n,k) = coefficient of x^(n-k) in F(x)*S(x)^(2*k-n). Here C(x)=(1-sqrt(1-4x))/(2*x) is o.g.f. for A000108, S(x)=(1-x-sqrt(1-6*x+x^2))/(2*x) is o.g.f. for A006318, and F(x)=S(x)/(1-x*C(x)*S(x)) is o.g.f. for A026781.
%Y Row-reversed or transposed version of A026780.
%Y Cf. A026781 (main diagonal), A026787 (sums of antidiagonals).
%K nonn,tabl
%O 0,5
%A _Max Alekseyev_, Jan 13 2015