%I #21 Apr 17 2023 06:49:19

%S 4,8,15,33,67,152,340,791,1845,4411,10557,25600,62332,152780,375859,

%T 928841,2302191,5724425,14269196,35655157,89277769,223982893,

%U 562912585,1417014038,3572323492,9018370892,22796073015,57691327693,146165207035,370706641856,941111617892,2391394225355,6081869637093

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

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

%H Z. Lengvárszky and Rick Mabry, <a href="https://doi.org/10.14232/actasm-016-789-y">Enumerating nets of prism-like polyhedra</a>, Acta Sci. Math. (Szeged) 83:3-4 (2017), 377-392.

%F 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

%t -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 *)

%o (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

%K nonn

%O 3,1

%A _Toshitaka Suzuki_, Mar 22 2005

%E More terms from _Rick Mabry_, Apr 10 2023

%E Definition changed by _Rick Mabry_, Apr 17 2023