cp's OEIS Frontend

A002986 Number of non-cyclic hydrocarbons with n carbon atoms (excluding stereoisomers).

%I A002986 M2376 #80 Jun 02 2025 15:48:55
%S A002986 1,3,4,12,27,84,247,826,2777,9868,35579,131847,495671,1893819,7320954,
%T A002986 28619581,112923053,449343946,1801330288,7269849395,29517342098,
%U A002986 120507480668,494449558111,2038073860257,8436185990286,35055744550563,146195133355612,611723431211193
%N A002986 Number of non-cyclic hydrocarbons with n carbon atoms (excluding stereoisomers).
%C A002986 a(n) is the number of hypothetical acyclic hydrocarbons with n carbon atoms that satisfy the octet rule. - _Natan Arie Consigli_, Dec 26 2016
%C A002986 a(n) is the number of acyclic connected multigraphs with n nodes of degree less than 5, except for a(2). - _Natan Arie Consigli_, May 25 2017
%D A002986 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002986 Andrew Howroyd, <a href="/A002986/b002986.txt">Table of n, a(n) for n = 1..500</a>
%H A002986 Sean A. Irvine, <a href="/A002986/a002986.java.txt">java program</a>
%H A002986 R. C. Read, <a href="/A002986/a002986.pdf">Some recent results in chemical enumeration</a>, Preprint, circa 1972. (Annotated scanned copy)
%H A002986 R. C. Read, <a href="http://dx.doi.org/10.1007/BFb0067377">Some recent results in chemical enumeration</a>, Lect. Notes Math. 303 (1972), 243-259.
%H A002986 Wikipedia, <a href="https://en.wikipedia.org/wiki/Graph_(discrete_mathematics)">Graph</a>
%F A002986 a(n) ~ c * d^n / n^(5/2), where d = 4.576467424512811226430711636719246756... and c = 0.84315686601314832608482486521039... - _Vaclav Kotesovec_, Feb 11 2019
%e A002986 a(3) = 4 because there are 4 non-cyclic structures that can be drawn with 3 carbons (propane, propene, propyne, and allene). - _David Consiglio, Jr._, May 15 2014
%o A002986 (nauty) geng -c -D4 ${n} $[${n}-1]:$[${n}-1] -q | multig -m3 -D4 -u
%o A002986 (PARI) \\ here S is MSET_k comb class of g
%o A002986 S(g,n,k)={polcoeff(exp( sum(i=1, k, (y^i + O(y*y^k))*subst(g + O(x*x^(n\i)), x, x^i)/i )), k, y) + O(x*x^n)}
%o A002986 R(n)={my(f,g,h); f=g=h=O(x); for(n=1, n, h = x*(1+f); g = h + x*(S(f,n,2) + g); f = g + x*(S(f,n,3) + f*g + h)); [f,g,h]}
%o A002986 seq(n)={my(t=R(n), f=t[1], g=t[2], h=t[3]); Vec(f + x*(S(f, n, 4) + g*S(f, n, 2) + S(g, n, 2) + f*h) + (subst(f+g+h+O(x*x^(n\2)), x, x^2) - f^2 - g^2 - h^2)/2)} \\ _Andrew Howroyd_, May 26 2018
%Y A002986 Cf. A000602 (restriction to alkanes).
%K A002986 nonn
%O A002986 1,2
%A A002986 _N. J. A. Sloane_
%E A002986 Better definition from _Sergio Pimentel_, Apr 28 2006
%E A002986 a(11) (computed using Nauty) from Vesa Linja-aho (vesa.linja-aho(AT)tkk.fi), Apr 24 2008
%E A002986 a(12)-a(13) (computed using Molgen 3.5) from _David Consiglio, Jr._, May 15 2014
%E A002986 Existing terms verified and a(14)-a(16) from _Sean A. Irvine_, Dec 22 2014
%E A002986 a(17)-a(19) from _Sean A. Irvine_, Dec 28 2014
%E A002986 a(18)-a(19) corrected and a(20)-a(24) (computed using nauty) from _Sean A. Irvine_, Jan 02 2015
%E A002986 Terms a(25) and beyond from _Andrew Howroyd_, May 26 2018