This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A039658 #32 Feb 16 2025 08:32:38
%S A039658 0,1,2,5,8,18,28,64,100,237,374,917,1460,3679,5898,15183,24468,64055,
%T A039658 103642,275011,446380,1197616,1948852,5277070,8605288,23483743,
%U A039658 38362198,105392983,172423768,476459938,780496108,2167743688,3554991268
%N A039658 Related to enumeration of edge-rooted catafusenes.
%C A039658 From _Petros Hadjicostas_, Jan 13 2019: (Start)
%C A039658 This sequence appears in Table I, p. 533, in Cyvin et al. (1992) and Table I, p. 1174, in Cyvin et al. (1994).
%C A039658 In Cyvin et al. (1992), it is defined through eq. (22), p. 535. We have a(n) = Sum_{i=1..n-1} M(i)*M(n-i), where M(2*n) = M(2*n-1) = A007317(n) for n >= 1.
%C A039658 In Cyvin et al. (1992), it is used in the calculation of sequence A026118. See eq. (34), p. 536, in Cyvin et al. (1992).
%C A039658 (The word "annelated" in the title of Cyvin et al. (1994) is spelled "annealated" in the text of Cyvin et al. (1992).)
%C A039658 (End)
%H A039658 Vincenzo Librandi, <a href="/A039658/b039658.txt">Table of n, a(n) for n = 1..1000</a>
%H A039658 S. J. Cyvin, Zhang Fuji, B. N. Cyvin, Guo Xiaofeng, and J. Brunvoll, <a href="https://pubs.acs.org/doi/pdfplus/10.1021/ci00009a021">Enumeration and classification of benzenoid systems. 32. Normal perifusenes with two internal vertices</a>, J. Chem. Inform. Comput. Sci., 32 (1992), 532-540.
%H A039658 S. J. Cyvin, B. N. Cyvin, J. Brunvoll, and E. Brendsdal, <a href="https://pubs.acs.org/doi/pdf/10.1021/ci00021a026">Enumeration and classification of certain polygonal systems representing polycyclic conjugated hydrocarbons: annelated catafusenes</a>, J. Chem. Inform. Comput. Sci., 34 (1994), 1174-1180.
%H A039658 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Fusene.html">Fusenes</a>.
%H A039658 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Polyhex.html">Polyhex</a>.
%F A039658 G.f.: (1+x)*(1 - 3*x^2 - sqrt(1 - 6*x^2 + 5*x^4))/(2*x^2*(1-x)) (eq. (9), p. 1175, in Cyvin et al. (1994)).
%F A039658 For n >= 1, a(n) = Sum_{i=1..n-1} A007317(floor((i+1)/2)) * A007317(floor((n-i+1)/2)). - _Petros Hadjicostas_, Jan 13 2019
%t A039658 Rest[CoefficientList[Series[(1+x) (1-3x^2-Sqrt[1-6x^2+5x^4])/(2x^2 (1-x)),{x,0,40}],x]] (* _Harvey P. Dale_, Oct 30 2016 *)
%Y A039658 Cf. A007317, A026118.
%K A039658 nonn
%O A039658 1,3
%A A039658 _N. J. A. Sloane_
%E A039658 More terms from _Emeric Deutsch_, Mar 14 2004