A126187 Sum of the levels of the first leaf (in the preorder traversal) over all hex trees with n edges.
3, 19, 96, 453, 2085, 9513, 43323, 197542, 903141, 4142565, 19067202, 88065360, 408108285, 1897265405, 8846769300, 41368049400, 193950461985, 911564782065, 4294230794520, 20273068467725, 95902496669091, 454528832324919
Offset: 1
Keywords
Links
- F. Harary and R. C. Read, The enumeration of tree-like polyhexes, Proc. Edinburgh Math. Soc. (2) 17 (1970), 1-13.
Crossrefs
Cf. A126186.
Programs
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Maple
g:=2*(1+3*z-sqrt(1-6*z+5*z^2))/(1-3*z+sqrt(1-6*z+5*z^2))^2: gser:=series(g,z=0,28): seq(coeff(gser,z,n),n = 1..25);
Formula
a(n) = Sum_{k=1..n} k*A126186(n,k).
G.f.: 2[1+3z-sqrt(1-6z+5z^2)]/[1-3z+sqrt(1-6z+5z^2)]^2.
D-finite with recurrence (n-1)*(3*n-1)*(n+4)*a(n) -n*(18*n^2+21*n-19)*a(n-1) +5*n*(3*n+2)*(n-1)*a(n-2)=0. - R. J. Mathar, Jun 17 2016
Comments