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A303840 Unlabeled trees with n nodes rooted at 2 indistinguishable roots that are leaves. 0
0, 1, 1, 2, 4, 10, 24, 63, 164, 444, 1204, 3328, 9233, 25865, 72734, 205656, 583320, 1660318, 4737540, 13551165, 38837535, 111512229, 320681604, 923528963, 2663057582, 7688068638, 22218350303, 64272720521, 186091334380, 539237928902, 1563731491958, 4537823968645, 13176960639940, 38286514506439, 111306880581963 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..35.

EXAMPLE

a(2)=a(3)=1, because the two roots must be the (all) leaves. a(4)=2 (one pattern from the linear tree, one from the star tree). a(6)=10: 1 pattern from n-Hexane. 2 patterns from 2-Methyl-Pentane. 2 patterns from (2,3)-Bimethyl-Butane. 1 pattern from the star graph. 2 patterns from 3-Methyl-Pentane. 2 patterns from (2,2)-Bimethyl-Butane.

MAPLE

a000081 := [1, 1, 2, 4, 9, 20, 48, 115, 286, 719, 1842, 4766, 12486, 32973, 87811, 235381, 634847, 1721159, 4688676, 12826228,

35221832, 97055181, 268282855, 743724984, 2067174645, 5759636510, 16083734329, 45007066269, 126186554308, 354426847597,

997171512998, 2809934352700, 7929819784355, 22409533673568, 63411730258053, 179655930440464, 509588049810620, 1447023384581029,

4113254119923150, 11703780079612453, 33333125878283632] ;

g81 := add( op(i, a000081)*x^i, i=1..nops(a000081) ) ;

g81fin := x ;

g := 0 ;

nmax := nops(a000081) ;

for m from 0 to nmax do

    mhalf := floor(m/2) ;

    ghalf := g81^mhalf*g81fin ;

    gcyc := (ghalf^2+subs(x=x^2, ghalf))/2 ;

    if type(m, odd) then

        gcyc := gcyc*g81 ;

    end if;

    g := g+gcyc ;

end do:

taylor(g, x=0, nmax) ;

gfun[seriestolist](%) ;

CROSSREFS

Cf. A303833 (roots need not be leaves), A055290 (cardinality of candidates).

Sequence in context: A138175 A121691 A124499 * A132220 A007874 A294410

Adjacent sequences:  A303837 A303838 A303839 * A303841 A303842 A303843

KEYWORD

nonn

AUTHOR

R. J. Mathar, May 01 2018

STATUS

approved

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Last modified June 26 00:10 EDT 2019. Contains 324367 sequences. (Running on oeis4.)