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%I #7 Jul 26 2019 09:24:17
%S 1,1,2,5,12,29,72,170,404,944,2184,5000,11368,25616,57376,127696,
%T 282688,622656,1365472,2982016,6488320,14068672,30409216,65536512,
%U 140859776,301990912,645924864,1378530048
%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^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
%p A122745 := proc(n)
%p local a,d ;
%p if n < 5 then
%p 1;
%p else
%p a := n-3 ;
%p if modp(a,3) = 0 then
%p d := 1 ;
%p else
%p d := 0 ;
%p end if;
%p # note the typo in last exponent in (31b)
%p (a+2)*(a+7)*2^(a-5)/3+2^floor(a/2-2) ;
%p %+d*2^(floor((a-3)/3))/3 ;
%p end if;
%p end proc:
%p seq(A122745(n),n=3..30) ; # _R. J. Mathar_, Jul 26 2019
%K nonn,easy
%O 3,3
%A _N. J. A. Sloane_, Sep 24 2006
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