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 A121102 Catapolyoctagons (see Cyvin et al. for precise definition). 2
 0, 0, 0, 4, 24, 144, 744, 3844, 19344, 97344, 487344, 2439844, 12202344, 61027344, 305152344, 1525839844, 7629277344, 38146777344, 190734277344, 953673339844, 4768368652344, 23841853027344, 119209274902344, 596046423339844, 2980232165527344, 14901161071777344, 74505805603027344 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 REFERENCES S. J. Cyvin, B. N. Cyvin, and J. Brunvoll. Enumeration of tree-like octagonal systems: catapolyoctagons, ACH Models in Chem. 134 (1997), 55-70, Table 1 Symmetry C_s. LINKS Table of n, a(n) for n=1..27. Index entries for linear recurrences with constant coefficients, signature (6,0,-30,25). FORMULA From R. J. Mathar, Jul 31 2019: (Start) G.f.: -4*x^4/((x - 1)*(5*x - 1)*(5*x^2 - 1)). 4*a(n) = 5^(n-2) + 1 - 10*A056487(n-4). (End) E.g.f.: (25*cosh(x) + cosh(5*x) - 10*cosh(sqrt(5)*x) + 25*sinh(x) + sinh(5*x) - 6*sqrt(5)*sinh(sqrt(5)*x) - 16)/100. - Stefano Spezia, Jun 06 2023 MAPLE A121102 := proc(n) local mr, ar, cr, dr , ir, p5; if n = 1 then ar := 1 ; else ar := 0 ; end if; dr := 1-ar ; p5 := 5^(floor(n/2)-1) ; if n = 1 then cr :=0 ; else cr := (p5-1)/2+2*ar/5 ; end if; mr := (3-2*(-1)^n)*p5/2-1/2 ; if n = 1 then ir := 1; else ir := (5^(n-2)+1)/4 +(2-(-1)^n)*p5/2 -3*ar/5 ; end if; ir-ar-dr-cr-mr ; end proc: seq(A121102(n), n=1..30) ; # R. J. Mathar, Jul 31 2019 MATHEMATICA LinearRecurrence[{6, 0, -30, 25}, {0, 0, 0, 4}, 27] (* Jean-François Alcover, Mar 31 2020 *) CROSSREFS Cf. A056487. Sequence in context: A005319 A155119 A114169 * A307526 A067411 A045915 Adjacent sequences: A121099 A121100 A121101 * A121103 A121104 A121105 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Aug 11 2006 STATUS approved

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Last modified November 30 02:55 EST 2023. Contains 367452 sequences. (Running on oeis4.)