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A228404 The number of complete binary trees with bicolored twigs. A twig is a vertex with one child on the boundary and the other child having no descendants. 1
1, 2, 8, 24, 76, 249, 836, 2860, 9932, 34918, 124032, 444448, 1604664, 5831765, 21316860, 78319140, 289064460, 1071275370, 3984871440, 14872552560, 55678270440, 209027020410, 786750047304, 2968257334104, 11223268563896, 42522737574604, 161415556062656, 613813414982656 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..27.

S. B. Ekhad, M. Yang, Proofs of Linear Recurrences of Coefficients of Certain Algebraic Formal Power Series Conjectured in the On-Line Encyclopedia Of Integer Sequences, (2017)

FORMULA

G.f.: 1 - x + 2*x*C^2 + x*C^4 where C is the g.f. for the Catalan numbers A000108.

Conjecture: -5*(n+3)*(n-2)*a(n) +5*(-n^2-n+18)*a(n-1) +5*(-n^2-n+48)*a(n-2) +(-5*n^2+20029*n+720)*a(n-3) +(-5*n^2-104153*n+186654)*

a(n-4) +(-5*n^2+130153*n-508806)*a(n-5) +13650*(2*n-11)*(n-7)*a(n-6)=0. - R. J. Mathar, Aug 08 2015

EXAMPLE

For n = 2 there are two complete binary trees. Both consist of two twigs so can be colored 4 ways each.

PROG

(PARI)

x = 'x + O('x^66);

C = serreverse( x/( 1/(1-x) ) ) / x; \\ Catalan A000108

gf = 1 - x + 2*x*C^2 + x*C^4;

Vec(gf) \\ Joerg Arndt, Aug 22 2013

CROSSREFS

Without the bicoloring A228403 is the result.

Cf. A000108.

Sequence in context: A130495 A026070 A093833 * A006952 A327550 A034741

Adjacent sequences:  A228401 A228402 A228403 * A228405 A228406 A228407

KEYWORD

nonn

AUTHOR

Louis Shapiro, Aug 21 2013

STATUS

approved

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Last modified January 24 04:35 EST 2020. Contains 331183 sequences. (Running on oeis4.)