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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

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 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.)