1,3

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.

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.

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.

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 (mathar(AT)strw.leidenuniv.nl), Feb 18 2008

Sequence in context: A164871 A079106 A088713 this_sequence A005394 A095818 A052397

Adjacent sequences: A135103 A135104 A135105 this_sequence A135107 A135108 A135109

more,nonn

R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 12 2008

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 18 2008