A103535 Number of nets in a regular right prism.

9, 29, 99, 354, 1290, 4762, 17663, 65733, 244923, 913383, 3407329, 12713796, 47443092, 177050612, 660741597, 2465886087, 9202736493, 34344949105, 128176812671, 478361888166, 1785269817246, 6662715837966, 24865590090907, 92799638767689, 346332952127775

Offset: 3

Author

Toshitaka Suzuki, Mar 22 2005

Keywords

• nonn

Comments

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

Links

• Takashi Horiyama and Wataru Shoji, The Number of Different Unfoldings of Polyhedra. In: L. Cai, S.-W. Cheng, and T.-W. Lam (Eds.): ISAAC2013, LNCS 8283, pp. 623-633, Springer-Verlag, 2013.

Formula

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

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

Extensions

More terms from Alois P. Heinz, Mar 31 2017