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A121126 Unbranched a-4-catapolynonagons (see Brunvoll reference for precise definition). 1
1, 4, 40, 330, 2814, 22464, 174798, 1321920, 9798840, 71383680, 512709912, 3638048256, 25547006016, 177770557440, 1227161345184, 8411086946304, 57284205913728, 387902612275200, 2613053064378240, 17519092525301760, 116946290184302592, 777543028253392896 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

LINKS

Colin Barker, Table of n, a(n) for n = 3..1000

J. Brunvoll, S. J. Cyvin and B. N. Cyvin, Isomer enumeration of polygonal systems representing polycyclic conjugated hydrocarbons: unbranched catacondensed systems with tetragons and q-gons, J. Molec. Struct. (Theochem), 364 (1996), 1-13, Table 12 with q=9 and alpha=3.

Index entries for linear recurrences with constant coefficients, signature (24,-204,576,1260,-9504,7776,31104,-46656).

FORMULA

G.f.: x^3 + 4*x^4 + 40*x^5 - 6*x^6*(-55 + 851*x - 3708*x^2 - 3273*x^3 + 54540*x^4 - 63828*x^5 - 178848*x^6 + 309096*x^7) / ( (6*x^2-1)^2*(6*x-1)^4 ). - R. J. Mathar, Aug 01 2019

a(n) = 24*a(n-1) - 204*a(n-2) + 576*a(n-3) + 1260*a(n-4) - 9504*a(n-5) + 7776*a(n-6) + 31104*a(n-7) - 46656*a(n-8) for n>13. - Colin Barker, Aug 03 2019

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

A121126 := proc(r::integer)

    q := 9 ;

    a := 3 ;

    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(A121126(n), n=3..30) ; # R. J. Mathar, Aug 01 2019

PROG

(PARI) Vec(x^3*(1 - 20*x + 148*x^2 - 390*x^3 - 510*x^4 + 3672*x^5 - 522*x^6 - 9288*x^7 - 5832*x^8 + 15552*x^9 + 11664*x^10) / ((1 - 6*x)^4*(1 - 6*x^2)^2) + O(x^30)) \\ Colin Barker, Aug 03 2019

CROSSREFS

Sequence in context: A190541 A298198 A043031 * A145730 A069721 A223176

Adjacent sequences:  A121123 A121124 A121125 * A121127 A121128 A121129

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Aug 13 2006

STATUS

approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)