A135106 Number of physical trees of alkane structures with n carbon vertices.
1, 1, 2, 6, 24, 118, 686, 4598, 34872, 295044, 2753958, 28103804, 311216626, 3716341042, 47597786154, 650812077852, 9461423560788, 145724617925326, 2370293673319292, 40600119927220706, 730458115445479734
Offset: 1
Keywords
Examples
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.
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.
Programs
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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
Formula
a(n) = A248837(n-2). - Georg Fischer, Oct 23 2018
Extensions
More terms from R. J. Mathar, Feb 18 2008
a(20)-a(21) from Alois P. Heinz, May 27 2013
Comments