A122742 Numbers of polypentagons with two connected internal vertices (see Cyvin et al. for precise definition).

0, 0, 1, 3, 6, 16, 34, 80, 172, 384, 824, 1792, 3824, 8192, 17376, 36864, 77760, 163840, 343936, 720896, 1507072, 3145728, 6553088, 13631488, 28310528, 58720256, 121632768, 251658240, 520089600, 1073741824, 2214584320, 4563402752, 9395224576, 19327352832, 39728414720, 81604378624

Offset: 4

Author

N. J. A. Sloane, Sep 24 2006

Keywords

• nonn
• easy

Links

• 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 (4,-2,-8,8).

Formula

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

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