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

3,1

Comments

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

Links

Table of n, a(n) for n=3..35.

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

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A018921 A305218 A321500 * A011970 A074025 A111988

Adjacent sequences: A103533 A103534 A103535 * A103537 A103538 A103539

Keyword

nonn

Author

Toshitaka Suzuki, Mar 22 2005

Extensions

More terms from Rick Mabry, Apr 10 2023

Definition changed by Rick Mabry, Apr 17 2023

Status

approved