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A038392 Mono-4-polyhexes. 3

%I

%S 1,1,2,6,19,71,274,1117,4650,19819,85710,375712,1664203,7439593,

%T 33515758,152019560,693625265,3181528275,14661581030,67850297506,

%U 315187646601,1469195636293,6869889703638,32215399021901,151467334017864,713881817440421,3372142139764434

%N Mono-4-polyhexes.

%D J. Brunvoll, B. N. Cyvin, and S. J. Cyvin, Studies of some chemically relevant polygonal systems: mono-q-polyhexes, ACH Models in Chem., 133 (3) (1996), 277-298; see Eq. 16.

%H Robert Israel, <a href="/A038392/b038392.txt">Table of n, a(n) for n = 1..1437</a>

%H S. J. Cyvin, <a href="https://doi.org/10.1016/0166-1280(92)85110-7">Graph-theoretical studies on fluoranthenoids and fluorenoids. Part 1</a>, Journal of Molecular Structure (Theochem), 262 (1992), 219-231.

%H N. Cyvin, E. Brendsdal, J. Brunvoll, S. J. Cyvin, <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.

%H S. J. Cyvin, B. N. Cyvin, J. Brunvoll and E. Brendsdal, <a href="https://doi.org/10.1021/ci00021a026">Enumeration and Classification of Certain Polygonal Systems Representing Polycyclic Conjugated Hydrocarbons: Annelated Catafusenes</a>, Journal of Chemical Information and Modeling [formerly, J. Chem. Inform. Comput. Sci.], 34 (1994), pp. 1174-1180.

%H S. J. Cyvin, B. N. Cyvin, J. Brunvoll, Zhang Fuji, Guo Xiaofeng, and R. Tosic, <a href="https://doi.org/10.1016/0166-1280(93)87033-A">Graph-theoretical studies on fluoranthenoids and fluorenoids: enumeration of some catacondensed systems</a>, Journal of Molecular Structures (Theochem), 285 (1993), 179-185.

%H 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.

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/Fusene.html">Fusene</a>, MathWorld-A Wolfram Web Resource.

%F G.f.: (2(1-z^2) - (1-z)f(z) - f(z^2))/(4(1-z)) where f(z) = sqrt(1-6z+5z^2). - _Emeric Deutsch_, Mar 14 2004

%F (250*n^2-250*n)*a(n)+(-300*n^2-150*n)*a(n+1)+(-325*n^2-875*n-600)*a(n+2)+(475*n^2+2045*n+2100)*a(n+3)+(35*n^2+265*n+540)*a(n+4)+(-193*n^2-1691*n-3660)*a(n+5)+(49*n^2+563*n+1596)*a(n+6)+(17*n^2+211*n+648)*a(n+7)+(-9*n^2-135*n-504)*a(n+8)+(n^2+17*n+72)*a(n+9) = 0. - _Robert Israel_, Oct 08 2017

%p f:= gfun:-rectoproc({(250*n^2-250*n)*a(n)+(-300*n^2-150*n)*a(n+1)+(-325*n^2-875*n-600)*a(n+2)+(475*n^2+2045*n+2100)*a(n+3)+(35*n^2+265*n+540)*a(n+4)+(-193*n^2-1691*n-3660)*a(n+5)+(49*n^2+563*n+1596)*a(n+6)+(17*n^2+211*n+648)*a(n+7)+(-9*n^2-135*n-504)*a(n+8)+(n^2+17*n+72)*a(n+9), a(0) = 0, a(1) = 1, a(2) = 1, a(3) = 2, a(4) = 6, a(5) = 19, a(6) = 71, a(7) = 274, a(8) = 1117},a(n),remember):

%p map(f, [$1..50]); # _Robert Israel_, Oct 08 2017

%t f[z_] := Sqrt[5*z^2 - 6*z + 1]; g[z_] := (2*(1 - z^2) - (1-z)*f[z] - f[z^2])/ (4*(1-z)); Drop[ CoefficientList[ Series[ g[z], {z, 0, 24}], z], 1] (* _Jean-Fran├žois Alcover_, Oct 13 2011, after _Emeric Deutsch_ *)

%Y Apart from initial term, (A002212 + A007317)/2. See A044045 for another version.

%K nonn,nice

%O 1,3

%A _N. J. A. Sloane_

%E More terms from _Emeric Deutsch_, Mar 14 2004

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Last modified October 14 07:15 EDT 2019. Contains 327995 sequences. (Running on oeis4.)