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

3,1

Comments

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

Links

Table of n, a(n) for n=3..27.

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

Crossrefs

Sequence in context: A198645 A045862 A035075 * A147268 A147376 A201447

Adjacent sequences: A103532 A103533 A103534 * A103536 A103537 A103538

Keyword

nonn

Author

Toshitaka Suzuki, Mar 22 2005

Extensions

More terms from Alois P. Heinz, Mar 31 2017

Status

approved