A122742 - OEIS

%I #11 Jul 26 2019 09:40:08

%S 0,0,1,3,6,16,34,80,172,384,824,1792,3824,8192,17376,36864,77760,

%T 163840,343936,720896,1507072,3145728,6553088,13631488,28310528,

%U 58720256,121632768,251658240,520089600,1073741824,2214584320,4563402752,9395224576,19327352832,39728414720,81604378624

%N Numbers of polypentagons with two connected internal vertices (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_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,-8,8).

%F G.f.: x^6*(x-1)*(2*x^3-4*x^2+1) / ((2*x-1)^2*(2*x^2-1)). - _Colin Barker_, Aug 29 2013

%F a(n) = A001787(n+1)/256 - 2^(n-7) - A077957(n)/16, n>6. - _R. J. Mathar_, Jul 26 2019

%K nonn,easy

%O 4,4

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