cp's OEIS Frontend

A121445 Triangle read by rows: T(n,k) is the number of ternary trees with n edges and such that the first leaf in the preorder traversal is at level k (1<=k<=n). A ternary tree is a rooted tree in which each vertex has at most three children and each child of a vertex is designated as its left or middle or right child.

%I A121445 #7 Apr 09 2013 09:41:53
%S A121445 3,3,9,10,18,27,42,69,81,81,198,312,351,324,243,1001,1540,1701,1566,
%T A121445 1215,729,5304,8034,8784,8100,6480,4374,2187,29070,43554,47313,43713,
%U A121445 35640,25515,15309,6561,163438,242896,262684,243108,200745,148716,96957
%N A121445 Triangle read by rows: T(n,k) is the number of ternary trees with n edges and such that the first leaf in the preorder traversal is at level k (1<=k<=n). A ternary tree is a rooted tree in which each vertex has at most three children and each child of a vertex is designated as its left or middle or right child.
%C A121445 Sum of terms in row n is A001764(n+1). T(n,1)=A121446(n) Sum(k*T(n,k),k=1..n)=A121447(n).
%F A121445 G.f.=G=G(t,z)=1/[1-t(h-1-z)/(h-1)]-1, where h=1+zh^3=2sin(arcsin(sqrt(27z/4))/3)/sqrt(3z).
%e A121445 T(1,1)=3 because we have the trees /, | and \.
%e A121445 T(2,1)=3 because we have the trees /|, /\ and |\.
%e A121445 Triangle starts:
%e A121445 3;
%e A121445 3,9;
%e A121445 10,18,27;
%e A121445 42,69,81;
%e A121445 198,312,351,324,243;
%p A121445 h:=2/sqrt(3*z)*sin(arcsin(sqrt(27*z/4))/3): G:=rationalize(1/(1-t*(h-1-z)/(h-1)))-1: Gser:=simplify(series(G,z=0,18)): for n from 1 to 10 do P[n]:=sort(expand(coeff(Gser,z^n))) od: for n from 1 to 10 do seq(coeff(P[n],t,j),j=1..n) od; # yields sequence in triangular form
%Y A121445 Cf. A001764, A121446, A121447.
%K A121445 nonn,tabf
%O A121445 1,1
%A A121445 _Emeric Deutsch_, Jul 30 2006
%E A121445 Keyword tabl changed to tabf by _Michel Marcus_, Apr 09 2013