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A122745 Numbers of polypentagons with one internal vertex (see Cyvin et al. for precise definition). 1
1, 1, 2, 5, 12, 29, 72, 170, 404, 944, 2184, 5000, 11368, 25616, 57376, 127696, 282688, 622656, 1365472, 2982016, 6488320, 14068672, 30409216, 65536512, 140859776, 301990912, 645924864, 1378530048 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,3

LINKS

Table of n, a(n) for n=3..30.

S. J. Cyvin et al., Theory of polypentagons, J. Chem. Inf. Comput. Sci., 33 (1993), 466-474

Index entries for linear recurrences with constant coefficients, signature (6,-10,-2,12,4,8,-48,32).

FORMULA

G.f. x^3+x^4+2*x^5+12*x^6 -x^7 *(12 -43*x +18*x^2 +52*x^3 +18*x^4 -32*x^5 -176*x^6 +160*x^7)  / ( (2*x^2-1) *(2*x^3-1) *(2*x-1)^3 ). - R. J. Mathar, Jul 26 2019

MAPLE

A122745 := proc(n)

    local a, d ;

    if n < 5 then

        1;

    else

        a := n-3 ;

        if modp(a, 3) = 0 then

            d := 1 ;

        else

            d := 0 ;

        end if;

        # note the typo in last exponent in (31b)

        (a+2)*(a+7)*2^(a-5)/3+2^floor(a/2-2) ;

        %+d*2^(floor((a-3)/3))/3 ;

    end if;

end proc:

seq(A122745(n), n=3..30) ; # R. J. Mathar, Jul 26 2019

CROSSREFS

Sequence in context: A131710 A227237 A005593 * A166292 A010374 A307788

Adjacent sequences:  A122742 A122743 A122744 * A122746 A122747 A122748

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Sep 24 2006

STATUS

approved

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Last modified October 2 06:43 EDT 2022. Contains 357191 sequences. (Running on oeis4.)