Revision History for A303840
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#14 by Joerg Arndt at Tue Jun 25 01:30:10 EDT 2024
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#13 by Michel Marcus at Tue Jun 25 00:58:42 EDT 2024
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#12 by Jon E. Schoenfield at Tue Jun 25 00:17:06 EDT 2024
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#11 by Jon E. Schoenfield at Tue Jun 25 00:16:51 EDT 2024
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| EXAMPLE
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a(2)=a(3)=1, because the two roots must be the (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.
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| STATUS
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approved
editing
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#10 by R. J. Mathar at Fri May 04 04:44:15 EDT 2018
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#9 by R. J. Mathar at Fri May 04 04:44:11 EDT 2018
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| CROSSREFS
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Cf. A303833 (roots mayneed not be leaves), A055290 (cardinality of candidates).
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| STATUS
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approved
editing
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#8 by R. J. Mathar at Tue May 01 13:00:17 EDT 2018
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#7 by R. J. Mathar at Tue May 01 11:35:00 EDT 2018
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Discussion
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| Tue May 01
| 12:23
| Omar E. Pol: I think the Name should starts with a(n) is the number of ..."
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#6 by R. J. Mathar at Tue May 01 11:34:49 EDT 2018
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| EXAMPLE
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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.
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#5 by R. J. Mathar at Tue May 01 11:28:21 EDT 2018
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| DATA
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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
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| MAPLE
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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](%) ;
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| CROSSREFS
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Cf. A303833 (roots may not be leaves), A055290. (cardinality of candidates).
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