A303840 - OEIS

A303840

Unlabeled trees with n nodes rooted at 2 indistinguishable roots that are leaves.

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 (all) the 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^mhalfg81fin ;` `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`