%I #12 Apr 07 2020 08:47:13

%S 0,0,1,4,10,27,67,166,396,934,2168,4984,11332,25584,57312,127624,

%T 282560,622528,1365200,2981760,6487808,14068128,30408192,65535488,

%U 140857664,301988864,645920768,1378525824,2936008704,6241120256,13242807552,28051496960,59324219392

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

%H S. J. Cyvin et al., <a href="https://doi.org/10.1021/ci00013a027">Theory of polypentagons</a>, J. Chem. Inf. Comput. Sci., 33 (1993), 466-474

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (6,-10,-2,12,4,8,-48,32).

%F 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

%p A := proc(n)

%p a := n-3 ;

%p if a < 2 then

%p 0;

%p elif a = 2 then

%p 1 ;

%p elif a =3 then

%p 4 ;

%p elif a > 3 then

%p if type(a,'odd') then

%p e := 0 ;

%p else

%p e := 1 ;

%p end if;

%p if type(a,'odd') then

%p epr := 1 ;

%p else

%p epr := 0 ;

%p end if;

%p if modp(a,3) = 0 then

%p d := 1 ;

%p else

%p d := 0 ;

%p end if;

%p # 3 append

%p (a-1)*(a-2)*2^(a-5)/3-epr*2^((a-5)/2)-d/3*2^((a-6)/3) ;

%p # 2 append

%p %+ ((a-1)*2^(a-2) -e*2^(a/2-1))/2 ;

%p # 1 append

%p %+ 2^(a-2) ;

%p end if;

%p end proc:

%p seq(A(n),n=3..40) ; # _R. J. Mathar_, Jul 26 2019

%t 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 *)

%K nonn,easy

%O 3,4

%A _N. J. A. Sloane_, Sep 24 2006