A122744 Numbers of polypentagons with one internal vertex (see Cyvin et al. for precise definition).

0, 0, 1, 4, 10, 27, 67, 166, 396, 934, 2168, 4984, 11332, 25584, 57312, 127624, 282560, 622528, 1365200, 2981760, 6487808, 14068128, 30408192, 65535488, 140857664, 301988864, 645920768, 1378525824, 2936008704, 6241120256, 13242807552, 28051496960, 59324219392

Offset

3,4

Links

Table of n, a(n) for n=3..35.

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^5+4*x^6 -x^7*(10 -33*x +5*x^2 +54*x^3 +4*x^4 -12*x^5 -136*x^6 +112*x^7) / ( (2*x^2-1) *(2*x^3-1) *(2*x-1)^3 ). - R. J. Mathar, Jul 26 2019

Maple

A := proc(n)
    a := n-3 ;
    if a < 2 then
        0;
    elif a = 2 then
        1 ;
    elif a =3 then
        4 ;
    elif a > 3 then
        if type(a, 'odd') then
            e := 0 ;
        else
            e := 1 ;
        end if;
        if type(a, 'odd') then
            epr := 1 ;
        else
            epr := 0 ;
        end if;
        if modp(a, 3) = 0 then
            d := 1 ;
        else
            d := 0 ;
        end if;
        # 3 append
        (a-1)*(a-2)*2^(a-5)/3-epr*2^((a-5)/2)-d/3*2^((a-6)/3) ;
        # 2 append
        %+ ((a-1)*2^(a-2) -e*2^(a/2-1))/2 ;
        # 1 append
        %+ 2^(a-2) ;
    end if;
end proc:
seq(A(n), n=3..40) ; # R. J. Mathar, Jul 26 2019

Mathematica

Join[{0, 0, 1, 4}, LinearRecurrence[{6, -10, -2, 12, 4, 8, -48, 32}, {10, 27, 67, 166, 396, 934, 2168, 4984}, 30]] (* Jean-François Alcover, Apr 07 2020 *)

Crossrefs

Sequence in context: A105999 A192210 A121494 * A192879 A077923 A183325

Adjacent sequences: A122741 A122742 A122743 * A122745 A122746 A122747

Keyword

nonn,easy

Author

N. J. A. Sloane, Sep 24 2006

Status

approved