

A296602


Values of F for which there is a unique convex polyhedron with F faces that are all regular polygons.


4



4, 19, 23, 25, 29, 31, 33, 35, 39, 41, 43, 45, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173
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OFFSET

1,1


COMMENTS

The main entry for this sequence is A180916.
All terms except 4 are odd, because both the cube and the pentagonal pyramid have 6 faces, and for any even F > 6 both a prism and an antiprism can have F faces. Platonic solids, Archimedean solids, Johnson solids, and prisms account for the missing odd numbers.


LINKS

Table of n, a(n) for n=1..75.
Index entries for linear recurrences with constant coefficients, signature (2,1).


FORMULA

A180916(a(n)) = 1.
From Colin Barker, Jul 05 2020: (Start)
G.f.: x*(4 + 11*x  11*x^2  2*x^3 + 2*x^4  2*x^5 + 2*x^8  2*x^9 + 2*x^12  2*x^13) / (1  x)^2.
a(n) = 2*a(n1)  a(n2) for n>14.
(End)


EXAMPLE

The regular tetrahedron is the only convex polyhedron with 4 faces that are all regular polygons, and no such polyhedron with fewer than 4 faces exists, so a(1) = 4.


MATHEMATICA

LinearRecurrence[{2, 1}, {4, 19, 23, 25, 29, 31, 33, 35, 39, 41, 43, 45, 49, 51}, 30] (* Georg Fischer, Oct 26 2020 *)


CROSSREFS

Cf. A180916, A242731, A296603, A296604.
Sequence in context: A012879 A072178 A116980 * A022135 A192193 A028564
Adjacent sequences: A296599 A296600 A296601 * A296603 A296604 A296605


KEYWORD

nonn,easy


AUTHOR

Jonathan Sondow, Jan 28 2018


STATUS

approved



