The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A300445 a(n) is the maximum value of the quartet index of a bifurcating rooted tree with n leaves. 0
 0, 0, 0, 1, 3, 9, 19, 38, 64, 106, 162, 243, 343, 479, 645, 860, 1110, 1424, 1790, 2237, 2743, 3349, 4035, 4842, 5734, 6770, 7920, 9239, 10679, 12315, 14105, 16120, 18290, 20716, 23342, 26257, 29377, 32821, 36517, 40574, 44880, 49586, 54602, 60059, 65827, 72079, 78705, 85860, 93376, 101468 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Grows asymptotically in O(n^4). LINKS T. M. Coronado, A. Mir, F. Rosselló, and G. Valiente, A balance index for phylogenetic trees based on quartets, arXiv preprint arXiv:1803.01651 [q-bio.PE], 2018. Tomás M. Coronado, Balance indices for phylogenetic trees under well-known probability models, Linköping University (Sweden, 2020). FORMULA a(n) = a(floor(n/2)) + a(ceiling(n/2)) + binomial(floor(n/2),2) * binomial(ceiling(n/2),2) for n>3; with a(1)=a(2)=a(3)=0. MATHEMATICA a[n_] := a[Floor[n/2]] + a[Ceiling[n/2]] + Binomial[Floor[n/2], 2]*Binomial[Ceiling[n/2], 2]; a[1] = 0; Array[a, 50] (* Robert G. Wilson v, Mar 06 2018 *) PROG (R) q=c(0, 0, 0, 1) for (i in (4:20)){q[i]=q[floor(i/2)] + q[ceiling(i/2)] + choose(floor(i/2), 2) * choose(ceiling(i/2), 2)} CROSSREFS Sequence in context: A146694 A146050 A147500 * A115238 A005994 A080010 Adjacent sequences: A300442 A300443 A300444 * A300446 A300447 A300448 KEYWORD nonn,easy AUTHOR Francesc Rosselló, Mar 06 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 31 13:56 EST 2023. Contains 359971 sequences. (Running on oeis4.)