A214205 Number of rooted planar binary unlabeled trees with n leaves and caterpillar index = 5.

0, 0, 0, 0, 0, 8, 0, 16, 64, 240, 832, 2976, 11008, 40624, 150400, 559584, 2090112, 7832928, 29432704, 110863680, 418479104, 1582628656, 5995379456, 22746329952, 86417102720, 328720669216, 1251831214976, 4772155518656, 18209463672320, 69544295350240, 265814912973056, 1016776398337728, 3892040452165888, 14907843267549376

Offset: 0

Author

N. J. A. Sloane, Jul 07 2012

Keywords

• nonn

Links

• Filippo Disanto, The size of the biggest Caterpillar subtree in binary rooted planar trees, arXiv preprint arXiv:1202.5668 [math.CO], 2012.
• Filippo Disanto, Unbalanced subtrees in binary rooted ordered and un-ordered trees, Séminaire Lotharingien de Combinatoire, 68 (2013), Article B68b.

Crossrefs

Cf. A025266, A000108, A025271, A214198-A214205.

Programs

Maple

C:=(1-sqrt(1-4*x))/2; # A000108 with a different offset
# F-(k): gives A025266, A025271, A214200, A214203
Fm:=k->(1/2)*(1-sqrt(1-4*x+2^(k+1)*x^(k+1)));
Sm:=k->seriestolist(series(Fm(k),x,50));
# F+(k): gives A000108, A214198, A214201, A214204
Fp:=k->C-Fm(k-1);
Sp:=k->seriestolist(series(Fp(k),x,50));
# F(k): gives A025266, A214199, A214202, A214205
F:=k->Fm(k)-Fm(k-1);
S:=k->seriestolist(series(F(k),x,50));

Mathematica

(1/2)*(Sqrt[1 - 4*x + 32*x^5] - Sqrt[1 - 4*x + 64*x^6]) + O[x]^34 // CoefficientList[#, x]& (* Jean-François Alcover, Nov 07 2016, after Maple *)