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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
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
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 549-554.
FORMULA
a(n) = A248837(n-2). - Georg Fischer, Oct 23 2018
EXAMPLE
Starting with a(1)=1, one C1 methane, we get a(2)=1, the C1-C2 backbone.
The third can be attached to either C1 ending up with C3-C1-C2, or to C2 ending up with C1-C2-C3, 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 := istack-1 ; 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: A336072 A328501 A328442 * A248837 A005394 A095818
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