A103535 - OEIS

%I #15 Mar 31 2017 11:48:14

%S 9,29,99,354,1290,4762,17663,65733,244923,913383,3407329,12713796,

%T 47443092,177050612,660741597,2465886087,9202736493,34344949105,

%U 128176812671,478361888166,1785269817246,6662715837966,24865590090907,92799638767689,346332952127775

%N Number of nets in a regular right prism.

%C The second term is the number of nets in a general regular right 4-prism, not in a cube.

%H Takashi Horiyama and Wataru Shoji, <a href="http://doi.org/10.1007/978-3-642-45030-3_58">The Number of Different Unfoldings of Polyhedra</a>. In: L. Cai, S.-W. Cheng, and T.-W. Lam (Eds.): ISAAC2013, LNCS 8283, pp. 623-633, Springer-Verlag, 2013.

%F a(n) = 1/(8*sqrt(3))*( 2*sqrt(3)*n + sqrt(3)*(2 + sqrt(3))^n + (2 + sqrt(3))^floor(n/2)*(4+2*sqrt(3)) + (2 - sqrt(3))^floor(n/2)*(2*sqrt(3) - 4) + sqrt(3)*((2 - sqrt(3))^n - 2)) for n >= 3 odd; a(n) = 1/24*(6*n + 3*(2 + sqrt(3))^n + 4*sqrt(3)*(2 + sqrt(3))^(n/2) - 4*sqrt(3)*(2 - sqrt(3))^(n/2) + 3*(2 - sqrt(3))^n - 6) for n >= 4 even. - _Humberto Bortolossi_, Mar 31 2017

%F Empirical g.f.: x^3*(9 - 25*x - 21*x^2 + 96*x^3 - 60*x^4 - 12*x^5 + 17*x^6 - 3*x^7) / ((1 - x)^2*(1 - 4*x + x^2)*(1 - 4*x^2 + x^4)). - _Colin Barker_, Mar 31 2017

%K nonn

%O 3,1

%A _Toshitaka Suzuki_, Mar 22 2005

%E More terms from _Alois P. Heinz_, Mar 31 2017