

A135106


Number of physical trees of alkane structures with n carbon vertices.


3



1, 1, 2, 6, 24, 118, 686, 4598, 34872, 295044, 2753958, 28103804, 311216626, 3716341042, 47597786154, 650812077852, 9461423560788, 145724617925326, 2370293673319292, 40600119927220706, 730458115445479734
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OFFSET

1,3


COMMENTS

Similar to A000602 (alkane trees with n carbon atoms) but keeping track of the history of attaching carbon atoms (methyls) to the backbone, as if these had been labeled.


LINKS

Table of n, a(n) for n=1..21.
J. V. Knop, W. R. Muller, K. Szymanski et al., Computer enumeration and generation of physical trees, J. Comput. Chem. vol. 8 no. 4 (1987) pp 549554.


FORMULA

a(n) = A248837(n2).  Georg Fischer, Oct 23 2018


EXAMPLE

Starting with a(1)=1, one C1 methane, we get a(2)=1, the C1C2 backbone.
The third can be attached to either C1 ending up with C3C1C2, or to C2 ending up with C1C2C3, yielding a(3)=2 different propanes.
C4 may be attached to any of C1 to C3 in these two propanes, yielding a(4)=6 different butanes, four of which are linear and two of which are stars.


MAPLE

A135106 := proc(n) local numb, stack, istack, N, i ; numb := array(1..n) ; for i from 1 to n do numb[i] := 0 ; od: stack := array(1..7, 1..100) ; stack[1, 1]:=2 ; stack[2, 1]:=0 ; stack[3, 1]:=0 ; stack[4, 1]:=0 ; stack[5, 1]:=1 ; stack[6, 1]:=0 ; stack[7, 1]:=1 ; istack := 1 ; while istack <> 0 do for i from 1 to 7 do stack[i, istack+1] := stack[i, istack] ; od: if stack[6, istack] = 3 then istack := istack1 ; else stack[6, istack] := stack[6, istack]+1 ; stack[1, istack+1] := stack[1, istack]+1 ; N := stack[6, istack] ; if stack[N, istack] <> 0 then stack[N, istack+1] := stack[N, istack+1]1 ; stack[N+1, istack+1] := stack[N+1, istack+1]+1 ; stack[5, istack+1] := stack[N, istack]*stack[5, istack] ; stack[6, istack+1] := 0 ; stack[7, istack+1] := stack[7, istack]+1 ; numb[stack[7, istack+1]]:=numb[stack[7, istack+1]]+stack[5, istack+1] ; if stack[7, istack+1] <> n then istack := istack+1 ; fi ; fi ; fi ; od: numb[n] ; end: for n from 2 do print( A135106(n)) ; end: # R. J. Mathar, Feb 18 2008


CROSSREFS

Sequence in context: A298432 A328501 A328442 * A248837 A005394 A095818
Adjacent sequences: A135103 A135104 A135105 * A135107 A135108 A135109


KEYWORD

nonn


AUTHOR

R. J. Mathar, Feb 12 2008


EXTENSIONS

More terms from R. J. Mathar, Feb 18 2008
a(20)a(21) from Alois P. Heinz, May 27 2013


STATUS

approved



