The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A323940 Number of nonisomorphic systems (isomers) for the unsymmetrical schemes (group C_s) for unbranched tri-4-catafusenes as a function of the number of hexagons (see Cyvin et al. (1996) for precise definition). 3
 0, 1, 8, 52, 244, 1093, 4490, 17952, 69304, 262385, 973916, 3562532, 12856716, 45880933, 162085694, 567578784, 1971766704, 6801381633, 23309759728, 79421199860, 269160256356, 907726205221, 3047449152562, 10188384019072, 33930769372904 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,3 COMMENTS See the comments of sequences A323939, A323941, and A323942 for explanations. - Petros Hadjicostas, May 26 2019 LINKS Georg Fischer, Table of n, a(n) for n = 3..103 S. J. Cyvin, B. N. Cyvin and J. Brunvoll, Isomer enumeration of some polygonal systems representing polycyclic conjugated hydrocarbons, Journal of Molecular Structure 376 (Issues 1-3) (1996), 495-505. See Table 1 on p. 500. Eric Weisstein's World of Mathematics, Fusene. Wikipedia, Molecular symmetry. Wikipedia, Point groups in three dimensions. Wikipedia, Polyhex (mathematics). Wikipedia, Schoenflies notation. Index entries for linear recurrences with constant coefficients, signature (14,-71,116,259,-1246,1013,2520,-5187,594,5931,-4428, -1215,2430,-729). FORMULA a(n) = (1/8) * (1 - (-1)^n) * ((n - 1) - (n + 3) * 3^((n - 5)/2)) + (1/8) * (n^2 + 11 * n + 12) * (n - 2) * 3^(n - 6) - (1/4) * binomial(n, 3) for n >= 3. - Petros Hadjicostas, May 26 2019 G.f.: x^4*(1 -6*x +11*x^2 -32*x^3 +182*x^4 -346*x^5 -122*x^6 +950*x^7 -831*x^8 +336*x^9 -297*x^10 +90*x^11) / ( (1+x)^2*(3*x^2-1)^2*(3*x-1)^4*(x-1)^4 ). - R. J. Mathar, Jul 25 2019 MAPLE # Calculates a(r) = AA(r), where r = n is the number of hexagons. # Crude numbers: JJ := proc(i) sum(binomial(j + 1, 3)*binomial(i - 2, j - 1)*2^(i - 1 - j), j = 1 .. i - 1); end proc; # Linearly annelated systems of D_{2h} symmetry: DD := proc(r) 1/4*(1 - (-1)^r)*(r - 1); end proc; # Linearly annelated systems of C_{2v} symmetry: LL := proc(r) 1/2*binomial(r, 3) - (1/8 - 1/8*(-1)^r)*(r - 1); end proc; # Centrosymmetrical (C_{2h}) systems: CC := proc(n) 1/24*(1 - (-1)^n)*((3 + n)*3^(1/2*n - 3/2) - 3*n + 3); end proc; # Total mirror-symmetrical (C_{2v}) systems: MM := proc(n) CC(n) + LL(n); end proc; # Unsymmetrical (C_s) systems: AA := proc(r) 1/4*(JJ(r) - DD(r) - 2*CC(r) - 2*MM(r)); end proc; # Generate sequence: for m from 3 to 100 do AA(m); end do; # Petros Hadjicostas, May 26 2019 MATHEMATICA LinearRecurrence[{14, -71, 116, 259, -1246, 1013, 2520, -5187, 594, 5931, -4428, -1215, 2430, -729}, {0, 1, 8, 52, 244, 1093, 4490, 17952, 69304, 262385, 973916, 3562532, 12856716, 45880933}, 100] (* from the g.f., Georg Fischer, Nov 07 2019 *) CROSSREFS Cf. A323939, A323941, A323942. Sequence in context: A244718 A303509 A107584 * A027225 A073377 A055283 Adjacent sequences:  A323937 A323938 A323939 * A323941 A323942 A323943 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Feb 09 2019 EXTENSIONS Name edited by Petros Hadjicostas, May 26 2019 More terms using various equations in Cyvin et al. (1996) from Petros Hadjicostas, May 26 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 19 18:35 EDT 2022. Contains 353847 sequences. (Running on oeis4.)