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%I #14 Jan 09 2015 17:32:39
%S 1,2,11,49,217,858,3314,11995,41921,141163,462674,1480017,4644331,
%T 14332801,43628996,131248423,390921934,1154427742,3384244322,
%U 9858374939,28560865688,82351168539,236465407302,676536049902,1929455222816
%N Number of isomers of alkyl homologs of adamantane with n carbon atoms.
%D M. Yu. Kornilov, Number of structural isomers in the adamantane series, J. Structural Chem. 16 (3) (1975), 466-468.
%H Alois P. Heinz, <a href="/A036996/b036996.txt">Table of n, a(n) for n = 0..700</a>
%F Reference gives a g.f.
%p A:= proc(n) option remember; unapply(`if`(n=0, 1, convert(series(1+ x/6 *(A(n-1)(x)^3 +3*A(n-1)(x) *A(n-1)(x^2) +2*A(n-1)(x^3)), x, n+1), polynom)), x) end: f:= (n,m)-> A(n)(x^m): gf:= n-> (f(n,1)^16 +3*f(n,2)^8 +8*f(n,1) *f(n,3)^5 +6*f(n,1)^4 *f(n,2)^6 +6*f(n,4)^4)/24: a:= n-> coeff(gf(n),x,n): seq(a(n), n=0..35); # _Alois P. Heinz_, Jul 29 2009
%t A[0] = 1&; A[n_][x_] := A[n][x] = Normal[Series[1+y/6*(A[n-1][y]^3+3*A[n-1][y]*A[n-1][y^2]+2*A[n-1][y^3]), {y, 0, n+1}]] /. y -> x; f[n_, m_] := A[n][x^m]; gf[n_] := (f[n, 1]^16+3*f[n, 2]^8+8*f[n, 1]*f[n, 3]^5+6*f[n, 1]^4*f[n, 2]^6+6*f[n, 4]^4)/24; a[n_] := Coefficient[gf[n], x, n]; Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, Feb 13 2014, after _Alois P. Heinz_'s Maple code *)
%Y Cf. A000598. - _Alois P. Heinz_, Jul 29 2009
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Alois P. Heinz_, Jul 29 2009
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