%I
%S 1,0,1,0,1,1,0,1,2,1,0,1,4,3,1,0,1,8,8,4,1,0,1,16,20,13,5,1,0,1,32,49,
%T 38,19,6,1,0,1,64,119,106,63,26,7,1,0,1,128,288,288,195,96,34,8,1,0,1,
%U 256,696,771,579,325,138,43,9,1,0,1,512,1681,2046,1675,1042,506,190,53
%N Triangle T(n,k) of number of integer sequences [y(1),...,y(n)] such that y(i)y(i+1)<=1, 1=y(1)<=y(i)<=k=y(n).
%F G.f. for column k: x^k/p(k) where p(0)=1, p(1)=1x, p(n)=(1x)p(n1)(x^2)p(n2).
%e Rows from n=0: {1}; {0,1}; {0,1,1}; {0,1,2,1}; {0,1,4,3,1}; ...
%e [1,1,1,2],[1,1,2,2],[1,2,1,2],[1,2,2,2] are the T(4,2)=4 sequences.
%o (PARI) T(n,k)=local(p0,p1,p2); if(k<0  k>n,0,p1=1; for(i=1,k,p2=(1x)*p1x^2*p0; p0=p1; p1=p2); polcoeff(x^k/p1+x*O(x^n),n))
%K nonn,tabl
%O 0,9
%A _Michael Somos_, Oct 01 2003
