A121447 Level of the first leaf (in preorder traversal) of a ternary tree, summed over all ternary trees with n edges. 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.
3, 21, 127, 747, 4386, 25897, 154077, 923910, 5581485, 33949836, 207787668, 1278900412, 7911394686, 49165322241, 306809507561, 1921849861260, 12079999018605, 76170034283805, 481680300300255, 3054157623774495
Offset: 1
Keywords
Examples
a(1)=3 because each of the trees /, | and \ contributes 1 to the sum.
Crossrefs
Cf. A121445.
Programs
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Maple
a:=n->3*n*(23*n^2+78*n+67)*binomial(3*n+2,n+2)/4/(n+3)/(2*n+1)/(2*n+3)/(2*n+5): seq(a(n),n=1..23);
Formula
a(n)=3n(23n^2+78n+67)binomial(3n+2,n+2)/[4(n+3)(2n+1)(2n+3)(2n+5)].
G.f.= (h-1-z)(h-1)/z^2, where h=1+zh^3=2sin(arcsin(sqrt(27z/4))/3)/sqrt(3z).
D-finite with recurrence -2*(2*n+5)*(n+3)*(1951*n-2094)*a(n) +(43553*n^3+142716*n^2+115045*n-10338)*a(n-1) +3*(2281*n+1723)*(3*n-1)*(3*n-2)*a(n-2)=0. - R. J. Mathar, Jul 24 2022
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