A000642 -id:A000642 - cp's OEIS frontend

A036671 Number of isomers C_n H_{2n} without double bonds.

0, 0, 1, 2, 5, 12, 29, 73, 185, 475, 1231, 3232, 8506, 22565, 60077, 160629, 430724, 1158502, 3122949, 8437289, 22836877, 61918923, 168139339, 457225555, 1244935251, 3393754661, 9261681937, 25301337669, 69184724389, 189349490641

Offset: 1

N. J. A. Sloane

Equivalently, the number of simple unicyclic graphs on n unlabeled vertices with all degrees at most 4. See table 1 in Michael A. Kappler reference. - Jonathan Vos Post, Dec 07 2005, Andrew Howroyd, May 22 2018

Camden A. Parks and James B. Hendrickson, Enumeration of monocyclic and bicyclic carbon skeletons, J. Chem. Inf. Comput. Sci., vol. 31, 334-339 (1991). See page 335 Table 1.
J. B. Hendrikson and C. A. Parks, "Generation and Enumeration of Carbon skeletons", J. Chem. Inf. Comput. Sci, vol. 31 (1991) pp. 101-107. See Table 2, column 3 on page 103.

Andrew Howroyd, Table of n, a(n) for n = 1..500
Michael A. Kappler, GENSMI: Exhaustive Enumeration of Simple Graphs.
G. Polya, Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen, Acta Math. 68 (1937), 145-254.

Cf. A000598, A000642, A001429.

\\ here G is A000598 as series
G(n)={my(g=O(x)); for(n=1, n, g = 1 + x*(g^3/6 + subst(g,x,x^2)*g/2 + subst(g,x,x^3)/3) + O(x^n)); g}
seq(n)={my(t=G(n-2)); t=x*(t^2+subst(t,x,x^2))/2; my(g(e)=subst(t + O(x*x^(n\e)), x, x^e) + O(x*x^n)); Vec(sum(k=3, n, sumdiv(k, d, eulerphi(d)*g(d)^(k/d))/k + if(k%2, g(1)*g(2)^(k\2), (g(1)^2+g(2))*g(2)^(k/2-1)/2))/2, -n)} \\ Andrew Howroyd, May 22 2018

Polya reference gives an explicit g.f.; so does Parks et al.

More terms from Vladeta Jovovic, Aug 19 2001

A002094 Number of unlabeled connected loop-less graphs on n nodes containing exactly one cycle (of length at least 2) and with all nodes of degree <= 4.

Original entry on oeis.org

0, 1, 2, 5, 10, 25, 56, 139, 338, 852, 2145, 5513, 14196, 36962, 96641, 254279, 671640, 1781840, 4742295, 12662282, 33898923, 90981264, 244720490, 659591378, 1781048728, 4817420360, 13050525328, 35405239155, 96180222540, 261603173201, 712364210543

Offset: 1

N. J. A. Sloane

nonn

A pair of parallel edges is permitted and is regarded as a cycle of length 2.
The original definition in A Handbook of Integer Sequences (1973) based on Schiff (1875) was simply "Alcohols". - N. J. A. Sloane, Mar 22 2018
Schiff used an now outdated terminology and did not use the term "alcohols", but in German "zweiwerthige Kohlenwasserstoffe C_{n}H_{2n} ..." and later "... deren je zwei verfuegbare Affinitaeten ... durch Alkoholradikale befriedigt sind.", translated "bivalent hydrocarbons ... whose free valences ... are covered by alcohol radicals". At that time the meaning of "alcohol radical" was different from modern terminology, now meaning an -OH group, but in Schiff's terminology another C_{x}H{y} hydrocarbon group was meant. The organic compounds that are described by the graphs of this sequence in modern chemical terminology are the acyclic alkenes, with exactly one double carbon-to-carbon bond, and the monocyclic cycloalkanes (see Wikipedia links). - Hugo Pfoertner, Mar 29 2018

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Vaclav Kotesovec, Table of n, a(n) for n = 1..400
R. J. Mathar, Illustration for graphs up to 6 carbons, 2018
Richard J. Mathar, Counting Connected Graphs without Overlapping Cycles, arXiv:1808.06264 [math.CO], 2018.
Hugo Schiff, Zur Statistik chemischer Verbindungen, Berichte der Deutschen Chemischen Gesellschaft, Vol. 8, pp. 1542-1547, 1875.
Hugo Schiff, Zur Statistik chemischer Verbindungen, Berichte der Deutschen Chemischen Gesellschaft, Vol. 8, pp. 1542-1547, 1875. [Annotated scanned copy]
Wikipedia, Alkene. Those with exactly one double carbon-to-carbon bond are covered by this sequence, the simplest being ethylene C_{2}H_{4}.
Wikipedia, Cycloalkane. The simplest alicyclic compounds, which are the monocyclic saturated hydrocarbons with formula C_{n}H_{2n}, are covered by this sequence, the first example being cyclopropane C_{3}H_{6}.

Cf. A000294, A000598, A000602, A000625, A000642, A001429 (unbound degrees), A068051.

# cycle index of cyclic group C_n
cycC_n := proc(n::integer,a)
    local d ;
    add(numtheory[phi](d)*a[d]^(n/d),d=numtheory[divisors](n)) ;
    %/n ;
end proc:
# cycle index of dihedral group
cyD_n := proc(n::integer,a)
    cycC_n(n,a)/2 ;
    if type(n,'odd') then
        %+ a[1]*a[2]^((n-1)/2)/2 ;
    else
        %+ ( a[1]^2*a[2]^((n-2)/2) +a[2]^(n/2) )/4 ;
    end if;
end proc:
a000642 := [
    1, 1, 2, 3, 7, 14, 32, 72, 171, 405, 989, 2426, 6045, 15167, 38422, 97925,
    251275, 648061, 1679869, 4372872, 11428365, 29972078, 78859809, 208094977,
    550603722, 1460457242, 3882682803, 10344102122, 27612603765, 73844151259,
    197818389539, 530775701520, 1426284383289] ;
g := [add(a000642[i]*x^i,i=1..nops(a000642)) ];
for i from 2 to nops(a000642) do
    g := [op(g), subs(x=x^i,g[1]) ] ;
end do:
Nmax := nops(a000642) :
G := 0 ;
for c from 2 to Nmax do
    f := cyD_n(c,g) ;
    G := G+ taylor(f,x=0,Nmax) ;
end do:
taylor(G,x=0,Nmax) ;
gfun[seriestolist](%) ; # R. J. Mathar, Mar 17 2018

terms = 31;
cycC[n_, a_] := Sum[EulerPhi[d] a[[d]]^(n/d), {d, Divisors[n]}]/n;
cyD[n_, a_] := Module[{cc}, cc = (1/2)cycC[n, a]; If[OddQ[n], (1/2)a[[1]]* a[[2]]^((n-1)/2)+cc, (1/4)(a[[1]]^2 a[[2]]^((n-2)/2) + a[[2]]^(n/2)) + cc]];
B[] = 0; Do[B[x] = Normal[(1/6) x (2 B[x^3] + 3 B[x^2] B[x] + B[x]^3) + O[x]^terms+1], terms];
A[x_] = (1/2) x (B[x^2] + B[x]^2) + O[x]^(terms+2);
a000642 = Rest[CoefficientList[A[x], x]];
g = {Sum[x^i a000642[[i]], {i, 1, terms+1}]};
For[i = 2, i <= Length[a000642], i++, g = Flatten[Append[g, g[[1]] /. x -> x^i]]];
For[G = 0; c = 2, c < terms+1, c++, f = cyD[c, g]; G = Series[f, {x, 0, terms+1}] + G];
Most[Rest[CoefficientList[G, x]]] (* Jean-François Alcover, Mar 26 2020, after R. J. Mathar *)

Let A(x) denote the generating function for A000598 (Number of rooted ternary trees with n nodes), i.e., A(x) = 1+(1/6)*x*(A(x)^3+3*A(x)*A(x^2)+2*A(x^3)), and set B(x)=(A(x)^2+A(x^2))/2. With D_k(x) being the cycle polynomial of the regular k-gon for k>=2, the final generating function is then given by Sum_{k>=2} x^k*D_k(B(x)), which can be evaluated very quickly. - Sascha Kurz, Mar 18 2018

Better definition from R. J. Mathar; terms beyond 852 from R. J. Mathar and Sean A. Irvine, Mar 17 2018

A000631 Number of ethylene derivatives with n carbon atoms.

Original entry on oeis.org

1, 1, 3, 5, 13, 27, 66, 153, 377, 914, 2281, 5690, 14397, 36564, 93650, 240916, 623338, 1619346, 4224993, 11062046, 29062341, 76581151, 202365823, 536113477, 1423665699, 3788843391, 10103901486, 26995498151, 72253682560, 193706542776

Offset: 2

N. J. A. Sloane

nonn

Number of structural isomers of alkenes C_n H_{2n} with n carbon atoms.
Number of unicyclic graphs of n nodes where a double-edge replaces the cycle, [A217781], end-points of the double-edge of out-degrees <= 2, other nodes having out-degrees <= 3.
Number of rooted trees on n+1 nodes where the root has degree 2, the 2 children of the root have out-degrees <= 2, and the other nodes have out-degrees <= 3.
See illustration of initial terms. - Washington Bomfim, Nov 30 2020

J. L. Faulon, D. Visco and D. Roe, Enumerating Molecules, In: Reviews in Computational Chemistry Vol. 21, Ed. K. Lipkowitz, Wiley-VCH, 2005.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Andrew Howroyd, Table of n, a(n) for n = 2..500
Washington Bomfim, Illustration of initial terms
J. L. Faulon, D. Visco and D. Roe, Enumerating Molecules, In: Reviews in Computational Chemistry Vol. 21, Ed. K. Lipkowitz, Wiley-VCH, 2005.
H. R. Henze and C. M. Blair, The number of structurally isomeric Hydrocarbons of the Ethylene Series, J. Amer. Chem. Soc., 55 (2) (1933), 680-686.
H. R. Henze and C. M. Blair, The number of structurally isomeric Hydrocarbons of the Ethylene Series, J. Amer. Chem. Soc., 55 (2) (1933), 680-685. (Annotated scanned copy)
H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1) (1934), 157-157.
C.-W. Lam, A Mathematical Relationship between the Number of Isomers of Alkenes and Alkynes: A Result Established from the Enumeration of Isomers of Alkenes from Alky Biradicals, J. Math. Chem., 23, 421 (1998).
R. J. Mathar, Illustration for graphs up to 6 carbons
R. C. Read, Some recent results in chemical enumeration, Lect. Notes Math. 303 (1972), 243-259.
R. C. Read, Some recent results in chemical enumeration, Preprint, circa 1972. (Annotated scanned copy)
R. C. Read, The Enumeration of Acyclic Chemical Compounds, pp. 25-61 of A. T. Balaban, ed., Chemical Applications of Graph Theory, Ac. Press, 1976. [Annotated scanned copy] See p. 28.
N. Trinajstich, Z. Jerievi, J. V. Knop, W. R. Muller and K. Szymanski, Computer Generation of Isomeric Structures, Pure & Appl. Chem., Vol. 55, No. 2, pp. 379-390, 1983.
Index entries for sequences related to rooted trees

Cf. A000642, A000598, A027852 (out-degrees of nodes not limited).

\\ Here G(n) is A000598 as g.f., h is A000642.
seq(n)={my(g=G(n), h=(subst(g, x, x^2) + g^2)/2); Vec(subst(h, x, x^2) + h^2)/2} \\ Andrew Howroyd, Dec 01 2020

a(n) = b(1)b(n-1) + b(2)b(n-2) + b(3)b(n-3) + ... + b(n/2)(b(n/2) + 1)/2 when n is even or b(1)b(n-1) + b(2)b(n-2) + b(3)b(n-3) + ... + b((n-1)/2)b((n + 1)/2) when n is odd, where b(n) = A000642(n). - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 24 2008
a(n) = Sum_{k=1..(n-1)/2}( f(k) * f(n-k) ) + [n mod 2 = 0] * ( f(n/2)^2 + f(n/2) ) / 2 where f(n) = A000642(n+1). - Washington Bomfim, Nov 29 2020
G.f.: (g(x^2) + g(x)^2)/2 where x*g(x) is the g.f. of A000642. - Andrew Howroyd, Dec 01 2020

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 24 2008

A261340 Decimal expansion of the radius of convergence of the generating function of A000598, the number of rooted ternary trees of n vertices.

Original entry on oeis.org

3, 5, 5, 1, 8, 1, 7, 4, 2, 3, 1, 4, 3, 7, 7, 3, 9, 2, 8, 8, 2, 2, 4, 4, 4, 7, 3, 6, 4, 7, 6, 3, 2, 6, 3, 6, 7, 0, 8, 7, 4, 6, 9, 5, 4, 1, 7, 5, 3, 2, 2, 1, 3, 4, 2, 3, 8, 1, 2, 9, 4, 9, 9, 7, 1, 2, 8, 0, 0, 1, 8, 0, 5, 7, 5, 5, 5, 7, 8, 2, 8, 8, 6, 7, 9, 8, 1, 3, 8, 1, 0, 8, 2, 4, 1, 6, 7

Offset: 0

Jean-François Alcover, Aug 15 2015

			0.35518174231437739288224447364763263670874695417532...

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6 Otter's tree enumeration constants, p. 298.

Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics, 2009; p. 478.

Cf. A000598, A000642, A002094, A121331, A244399.

digits = 97; m = 2 digits + 10; For[gf = 0; i = 0, i <= m, i++, gf = Series[1 + x*(gf^3/6 + (gf /. x -> x^2)*gf/2 + (gf /. x -> x^3)/3), {x, 0, m + 1}] // Normal];
g[r_] := Module[{r2, r3, X, ym}, r2 = gf /. x -> r^2; r3 = gf /. x -> r^3; X[y_] = (y - 1)/(y^3/6 + r2*y/2 + r3/3); ym = y /. FindRoot[X'[y] == 0, {y, 2}, WorkingPrecision -> digits + 5]; X[ym]]; rho = FixedPoint[g, 1/3, SameTest -> (Abs[#1 - #2] < 10^-digits &)]; RealDigits[rho, 10, digits] // First

More digits from Vaclav Kotesovec, Aug 15 2015

More digits and Mma code updated by Jean-François Alcover, Apr 18 2016

A000635 Number of paraffins C_n H_{2n} X Y with n carbon atoms.

Original entry on oeis.org

0, 1, 2, 5, 12, 31, 80, 210, 555, 1479, 3959, 10652, 28760, 77910, 211624, 576221, 1572210, 4297733, 11767328, 32266801, 88594626, 243544919, 670228623, 1846283937, 5090605118, 14047668068, 38794922293, 107215238057, 296501478704

Offset: 0

N. J. A. Sloane

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 0..200
Frederic Chyzak, Enumerating alcohols and other classes of chemical molecules
H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1) (1934), 157-157.
H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1) (1934), 157-157. (Annotated scanned copy)
G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; Table I line 3.
G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; Table I, line 3. (Annotated scanned copy)
R. C. Read, The Enumeration of Acyclic Chemical Compounds, pp. 25-61 of A. T. Balaban, ed., Chemical Applications of Graph Theory, Ac. Press, 1976. [Annotated scanned copy] See p. 28.

terms = 29; B[] = 0; Do[B[x] = 1 + (1/6)*x*(B[x]^3 + 3*B[x]*B[x^2] + 2*B[x^3]) + O[x]^terms // Normal, terms];
B642[x_] = (1/2)*x*(B[x^2] + B[x]^2) + O[x]^terms;
A[x_] = B642[x]/(1 - B642[x]);
CoefficientList[A[x], x] (* Jean-François Alcover, Oct 21 2011, updated Jan 10 2018 *)

G.f.: A(x) = B(x)/(1-B(x)), B(x) = g.f. for A000642.

A000636 Number of paraffins C_n H_{2n} X_2 with n carbon atoms.

Original entry on oeis.org

1, 2, 4, 9, 21, 52, 129, 332, 859, 2261, 5983, 15976, 42836, 115469, 312246, 847241, 2304522, 6283327, 17164401, 46972357, 128741107, 353345434, 970999198, 2671347292, 7356752678, 20279171785, 55948407837, 154479213626, 426845422807, 1180229767202

Offset: 1

N. J. A. Sloane

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1) (1934), 157-157.
H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1) (1934), 157-157. (Annotated scanned copy)
G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; line 4 of Table I.
G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; Table I, line 2. (Annotated scanned copy)
R. C. Read, The Enumeration of Acyclic Chemical Compounds, pp. 25-61 of A. T. Balaban, ed., Chemical Applications of Graph Theory, Ac. Press, 1976. [Annotated scanned copy] See p. 28.

G.f.: (1/2) * (1/(1-x*R(x)) + (1+x*R(x)) / (1-x^2*R(x^2))) where R(x) is the g.f. for A000642 [From Polya paper]. - Sean A. Irvine, Oct 04 2016

More terms from Sean A. Irvine, Oct 04 2016

A000640 Number of paraffins C_n H_{2n-1} XYZ with n carbon atoms.

Original entry on oeis.org

0, 1, 4, 13, 42, 131, 402, 1218, 3657, 10899, 32298, 95257, 279844, 819390, 2392392, 6967956, 20250974, 58744089, 170118980, 491913999, 1420493862, 4096940530, 11803172152, 33970257473, 97678027311, 280624328431, 805587723862

Offset: 0

N. J. A. Sloane

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, Table of n, a(n) for n = 0..100
Frederic Chyzak, Enumerating alcohols and other classes of chemical molecules
G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443.
G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443. (Annotated scanned copy)

Cf. A000598, A000642.

# The following Maple commands are taken from the Chyzak web site:
with(combstruct);
gramm_Alkyl:=Alkyl=Prod(Carbon,Set(Alkyl,card<=3)),Carbon=Atom:
specs_Alkyl:=[Alkyl,{gramm_Alkyl},unlabeled]:
gramm_S1_Alkyl:=S1_Alkyl[X]=Union(Prod(Carbon,S1_Alkyl[X],Set(Alkyl,card<=2)),Prod(Prod(Carbon,X),Set(Alkyl,card<=2))),X=Epsilon:
specs_S1_Alkyl:=[S1_Alkyl[X],{gramm_S1_Alkyl,gramm_Alkyl},unlabeled]:
gramm_S2_Alkyl:=S2_Alkyl[X,Y]=Union(Prod(Carbon,S2_Alkyl[X,Y], Set(Alkyl,card<=2)),Prod(Carbon,Union(S1_Alkyl[X],X),Union(S1_Alkyl[Y],Y),Set(Alkyl,card<=1))):
specs_S2_Alkyl:=[S2_Alkyl[X,Y],{gramm_S2_Alkyl,gramm_S1_Alkyl,op(subs(X=Y,[gramm_S1_Alkyl])),gramm_Alkyl},unlabeled]:
[seq(count(specs_S2_Alkyl,size=i),i=0..50)];

terms = 27; (* B,B2 = g.f. for A000598,A000642 resp. *) B[] = 0; Do[B[x] = 1 + (1/6)*x*(B[x]^3 + 3*B[x]*B[x^2] + 2*B[x^3]) + O[x]^terms // Normal, terms];
B2[x_] = (1/2)*x*(B[x^2] + B[x]^2) + O[x]^terms;
A[x_] = x*B[x]/(1 - B2[x])^3 + O[x]^terms;
CoefficientList[A[x], x] (* Jean-François Alcover, Jan 10 2018 *)

G.f.: A(x) = x*A000598(x)/(1-A000642(x))^3.

A000641 Number of paraffins C_n H_{2n-1} X_3 with n carbon atoms.

Original entry on oeis.org

0, 1, 2, 5, 14, 39, 109, 312, 890, 2552, 7325, 21047, 60465, 173750, 499068, 1433071, 4113105, 11799780, 33834367, 96968462, 277771344, 795310628, 2276055442, 6510786627, 18616389094, 53207964655, 152014267327, 434136228215

Offset: 0

N. J. A. Sloane

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; line 7 of Table I.
G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; Table I, line 7. (Annotated scanned copy)
G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; Table I, line 7. (Annotated scanned copy)

G.f.: A(x) = ((x*r)/6)*( 1/(1-x*R)^3 + 3/((1-x*R)*(1-x^2*R2)) + 2/(1-x^3*R3)); r = A000598(x), R=A000642(x)/x, Ri=R(x^i).

A022014 Tri-substituted alkanes of form C_n H_{2n-1} X_2 Y, or equivalently bi-substituted alkyls of form -C_n H_{2n-1} X_2 (n=1: CHXXY; n=2: CXXY-CHHH CXYH-CXHH CXXH-CYHH).

Original entry on oeis.org

0, 1, 3, 9, 27, 81, 240, 711, 2094, 6152, 18012, 52613, 153297, 445772, 1293780, 3748820, 10845935, 31336532, 90426198, 260644262, 750502831, 2158961013, 6205225334, 17820505454, 51139664497, 146654181925, 420291420558

Offset: 0

N. J. A. Sloane, Paul Zimmermann

nonn

Sean A. Irvine, Java program (github)
G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; line 6 of Table I.
G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; Table I, line 6. (Annotated scanned copy)

Cf. A000598, A000641, A000642.

G.f.: (1/2) * (x*r(x)/(1-x*R(x)) * (1/(1-x*R(x))^2 + 1/(1-x^2*R(x^2))) where r(x) is the g.f. for A000598 and R(x) is the g.f. for A000642 [from Polya, p. 440]. - Sean A. Irvine, May 13 2019

A000634 Number of glycols with n carbon atoms.

Original entry on oeis.org

1, 2, 6, 14, 38, 97, 260, 688, 1856, 4994, 13550, 36791, 100302, 273824, 749316, 2053247, 5635266, 15484532, 42599485, 117312742, 323373356, 892139389, 2463252315, 6806148956, 18818714543, 52065725034, 144135111504, 399232819042, 1106385615943

Offset: 2

N. J. A. Sloane

nonn

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1) (1934), 157-157.
H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1) (1934), 157-157. (Annotated scanned copy)
R. C. Read, The Enumeration of Acyclic Chemical Compounds, pp. 25-61 of A. T. Balaban, ed., Chemical Applications of Graph Theory, Ac. Press, 1976. [Annotated scanned copy] See p. 28.

Cf. A000636, A000642.

a(n) = A000636(n) - A000642(n). - Sean A. Irvine, Nov 18 2016

More terms from Sean A. Irvine, Nov 18 2016

cp's OEIS Frontend

A036671 Number of isomers C_n H_{2n} without double bonds.

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A002094 Number of unlabeled connected loop-less graphs on n nodes containing exactly one cycle (of length at least 2) and with all nodes of degree <= 4.

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A000631 Number of ethylene derivatives with n carbon atoms.

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A261340 Decimal expansion of the radius of convergence of the generating function of A000598, the number of rooted ternary trees of n vertices.

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A000635 Number of paraffins C_n H_{2n} X Y with n carbon atoms.

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A000636 Number of paraffins C_n H_{2n} X_2 with n carbon atoms.

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A000640 Number of paraffins C_n H_{2n-1} XYZ with n carbon atoms.

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A000641 Number of paraffins C_n H_{2n-1} X_3 with n carbon atoms.

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