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 A121124 Unbranched a-4-catapolynonagons (see Brunvoll reference for precise definition). 1
 1, 4, 21, 138, 864, 5526, 34992, 221724, 1399680, 8818632, 55427328, 347684400, 2176782336, 13604912928, 84894511104, 528958247616, 3291294892032, 20453047668864, 126949945835520, 787089669219072, 4874877920083968, 30163307160752640, 186464080443211776, 1151689908801235968 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 LINKS J. Brunvoll, S. J. Cyvin and B. N. Cyvin, Isomer enumeration of polygonal systems..., J. Molec. Struct. (Theochem), 364 (1996), 1-13, Table 12, q=9, alpha=1. Index entries for linear recurrences with constant coefficients, signature (12,-30,-72,216). FORMULA From R. J. Mathar, Aug 01 2019: (Start) G.f.: x^2 +4*x^3 -3*x^4*(7-38*x-54*x^2+270*x^3) / ( (6*x^2-1)*(-1+6*x)^2 ). a(n) = A000400((n-1)/2)/12 +6^(n-1)/16 +A053469(n+1)/864, where Axxxxx(.) is zero for fractional indices, n>3. (End) MAPLE # Exhibit 1 Hra := proc(r::integer, a::integer, q::integer)     binomial(r-1, a-1)*(q-3)+binomial(r-1, a) ;     %*(q-3)^(r-a-1) ; end proc: Jra := proc(r::integer, a::integer, q::integer)     binomial(r-2, a-2)*(q-3)^2 +2*binomial(r-2, a-1)*(q-3) +binomial(r-2, a) ;     %*(q-3)^(r-a-2) ; end proc: # Exhibit 2 A121124 := proc(r::integer)     q := 9 ;     a := 1 ;     Jra(r, a, q)+binomial(2, r-a)+( 1 +(-1)^(r+a) +(1+(-1)^a)*(1-(-1)^r)*floor((q-3)/2)/2)*Hra(floor(r/2), floor(a/2), q) ;     %/4 ; end proc: seq(A121124(n), n=2..30)  # R. J. Mathar, Aug 01 2019 MATHEMATICA Join[{1, 4}, LinearRecurrence[{12, -30, -72, 216}, {21, 138, 864, 5526}, 22]] (* Jean-François Alcover, Apr 04 2020 *) CROSSREFS Sequence in context: A288869 A288268 A265952 * A180399 A222058 A265174 Adjacent sequences:  A121121 A121122 A121123 * A121125 A121126 A121127 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Aug 13 2006 STATUS approved

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Last modified September 23 12:43 EDT 2021. Contains 347617 sequences. (Running on oeis4.)