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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 (list; graph; refs; listen; history; text; internal format)
 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: 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

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Last modified November 14 17:24 EST 2019. Contains 329126 sequences. (Running on oeis4.)