login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A038078 Number of identity trees with 2-colored nodes. 3
1, 2, 1, 2, 6, 20, 69, 270, 1026, 4120, 16794, 70230, 298306, 1288912, 5642559, 25007756, 111998920, 506348902, 2308338456, 10602357346, 49026021552, 228085486580, 1067020210339, 5016982766202, 23698640081356, 112422573858292, 535414026652828, 2559204304109868 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

Index entries for sequences related to trees

FORMULA

G.f.: B(x) - B^2(x)/2 - B(x^2)/2, where B(x) is g.f. for A038077.

a(n) ~ c * d^n / n^(5/2), where d = A246312 = 5.2490324912281705791649522161843092..., c = 0.356142078281568492877259973613... . - Vaclav Kotesovec, Sep 06 2014

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

      add(binomial(2*b(i-1$2), j)*b(n-i*j, i-1), j=0..n/i)))

    end:

a:= n-> `if`(n=0, 1, 2*b(n-1$2) -2*add(b(j-1$2)*b(n-j-1$2)

        , j=1..n-1) -`if`(irem(n, 2, 'r')=0, b(r-1$2), 0)):

seq(a(n), n=0..35);  # Alois P. Heinz, Aug 02 2013

MATHEMATICA

b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[2*b[i-1, i-1], j]*b[n-i*j, i-1], {j, 0, n/i}]]];

a[n_] := If[n==0, 1, 2*b[n-1, n-1] - 2*Sum[b[j-1, j-1]*b[n-j-1, n-j-1], {j, 1, n-1}] - If[Mod[n, 2]==0, r=n/2; b[r-1, r-1], 0]];

Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Mar 01 2016, after Alois P. Heinz *)

CROSSREFS

Cf. A000220. A038077-A038080.

Cf. A246312.

Sequence in context: A170829 A032085 A032163 * A000139 A302190 A114572

Adjacent sequences:  A038075 A038076 A038077 * A038079 A038080 A038081

KEYWORD

nonn

AUTHOR

Christian G. Bower, Jan 04 1999

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 16 15:55 EST 2020. Contains 331961 sequences. (Running on oeis4.)