cp's OEIS Frontend

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.

A044046 Nonisomorphic catacondensed monoheptafusenes (see reference for precise definition).

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%I A044046 #20 Jun 26 2022 23:56:03
%S A044046 0,0,1,3,16,66,300,1314,5884,26304,118633,537255,2447172,11197710,
%T A044046 51473017,237569535,1100655430,5117008440,23865566651,111636805905,
%U A044046 523632748312,2462303017950,11605730134178,54821137926588,259479816361256,1230496691745816,5845551200648015
%N A044046 Nonisomorphic catacondensed monoheptafusenes (see reference for precise definition).
%H A044046 S. J. Cyvin, J. Brunvoll, and B. N. Cyvin, <a href="https://doi.org/10.1007/BF01172927">Harary-Read numbers for catafusenes: Complete classification according to symmetry</a>, Journal of mathematical chemistry 9.1 (1992): 19-31.
%H A044046 S. J. Cyvin, J. Brunvoll, <a href="https://doi.org/10.1007/BF01172928">Generating functions for the Harary-Read numbers classified according to symmetry</a>, Journal of mathematical chemistry 9.1 (1992): 33-38.
%H A044046 B. N. Cyvin et al., <a href="http://dx.doi.org/10.1007/BF00811082">A class of polygonal systems representing polycyclic conjugated hydrocarbons: Catacondensed monoheptafusenes</a>, Monat. f. Chemie, 125 (1994), 1327-1337 (see Table 1).
%H A044046 S. J. Cyvin et al., <a href="http://dx.doi.org/10.1016/0166-1280(93)87033-A">Graph-theoretical studies on fluoranthenoids and fluorenoids:enumeration of some catacondensed systems</a>, J. Molec. Struct. (Theochem), 285 (1993), 179-185.
%H A044046 S. J. Cyvin et al., <a href="http://dx.doi.org/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 A044046 F. Harary and R. C. Read, <a href="https://doi.org/10.1017/S0013091500009135">The enumeration of tree-like polyhexes</a>, Proc. Edinburgh Math. Soc. (2) 17 (1970), 1-13.
%F A044046 From _Emeric Deutsch_, Mar 14 2004: (Start)
%F A044046 G.f.: (U(z)^2 + U(z^2))/2, where U(z) = (1 - 3z - sqrt(1 - 6z + 5z^2))/(2z). [corrected by _Michel Marcus_, Apr 22 2019]
%F A044046 a(2n) = (1/2)*(A045445(2n) + A002212(n)), n >= 1; a(2n+1) = (1/2)*A045445(2n+1), n >= 0. (End)
%o A044046 (PARI) U(z)= (1-3*z-sqrt(1-6*z+5*z^2))/(2*z);
%o A044046 my(x='x + O('x^40)); concat([0, 0], Vec((U(z)^2 + U(z^2))/2)) \\ _Michel Marcus_, Apr 22 2019
%Y A044046 Cf. A002212, A045445, A045904, A121070. Equals A121071/2.
%K A044046 nonn
%O A044046 0,4
%A A044046 _N. J. A. Sloane_
%E A044046 More terms from _Emeric Deutsch_, Mar 14 2004
%E A044046 More terms from _Michel Marcus_, Apr 22 2019