A103536 Number of geometrically distinct edge-unfoldings of a regular n-gonal pyramid.

4, 8, 15, 33, 67, 152, 340, 791, 1845, 4411, 10557, 25600, 62332, 152780, 375859, 928841, 2302191, 5724425, 14269196, 35655157, 89277769, 223982893, 562912585, 1417014038, 3572323492, 9018370892, 22796073015, 57691327693, 146165207035, 370706641856, 941111617892, 2391394225355, 6081869637093

Offset: 3

Author

Toshitaka Suzuki, Mar 22 2005

Keywords

• nonn

Comments

The first term is the number of nets of a general regular triangular pyramid, not of a tetrahedron.

Links

• Z. Lengvárszky and Rick Mabry, Enumerating nets of prism-like polyhedra, Acta Sci. Math. (Szeged) 83:3-4 (2017), 377-392.

Programs

Mathematica

-1 + (1/2) Fibonacci[n] + (1/(2 n)) Sum[Fibonacci[2 GCD[j, n] - 1] + Fibonacci[2 GCD[j, n] + 1], {j, 1, n}] (* Rick Mabry, Apr 10 2023 *)

PARI

a(n) = {sum(j=1, n, fibonacci(2*gcd(j,n) - 1) + fibonacci(2*gcd(j,n) + 1))/(2*n) + fibonacci(n)/2 - 1} \\ Andrew Howroyd, Apr 10 2023

Formula

a(n) = -1 + (1/2)*F(n) + (1/(2*n))*Sum_{j=1..n} (F(2*gcd(j,n)-1) + F(2*gcd(j,n)+1)), where F(n) is the usual n-th Fibonacci number. Simplified from link. - Rick Mabry, Apr 10 2023

Extensions

More terms from Rick Mabry, Apr 10 2023

Definition changed by Rick Mabry, Apr 17 2023