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A005960 Number of acyclic disubstituted alkanes with n carbon atoms and distinct substituents.
(Formerly M2747)

%I M2747

%S 1,3,8,23,69,208,636,1963,6099,19059,59836,188576,596252,1890548,

%T 6008908,19139155,61074583,195217253,624913284,2003090071,6428430129,

%U 20653101216,66420162952,213802390264,688796847976,2220789746752,7165331870036

%N Number of acyclic disubstituted alkanes with n carbon atoms and distinct substituents.

%C Acyclic alkanes of the form C_nH_mXY with X != Y. For X = Y see A005961. - _Sean A. Irvine_, Nov 12 2016

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H R. C. Read, <a href="/A000598/a000598.pdf">The Enumeration of Acyclic Chemical Compounds</a>, pp. 25-61 of A. T. Balaban, ed., Chemical Applications of Graph Theory, Ac. Press, 1976. [Annotated scanned copy] See p. 44.

%F G.f.: 1/(1-x*B(x)^2) where B(x) is the g.f. for A000625. - _Sean A. Irvine_, Nov 12 2016

%t terms = 27; (* B = g.f. for A000625 *) B[_] = 0; Do[B[x_] = 1 + x*((B[x]^3 + 2*B[x^3])/3) + O[x]^(terms + 1) // Normal, terms + 1];

%t A[x_] = 1/(1 - x*B[x]^2) + O[x]^(terms + 1);

%t CoefficientList[A[x], x] // Rest (* _Jean-Fran├žois Alcover_, Jan 10 2018 *)

%Y Cf. A193418.

%K nonn

%O 1,2

%A _N. J. A. Sloane_

%E More terms and title improved by _Sean A. Irvine_, Nov 12 2016

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Last modified December 14 22:42 EST 2019. Contains 329987 sequences. (Running on oeis4.)