A128112 Number of uniform polyhedra with n faces.

0, 0, 0, 1, 1, 1, 3, 3, 3, 4, 3, 10, 5, 7, 6, 7, 4, 11, 8, 12, 9, 8, 6, 16, 11, 13, 10, 14, 9, 10, 14, 19, 15, 13, 10, 19, 12, 11, 18, 21, 12, 16, 20, 20, 21, 16, 12, 26, 23, 14, 21, 25, 16, 22, 26, 21, 20, 20, 18, 33, 29, 18, 30, 35, 18, 27, 24, 23, 33, 26, 22, 28, 35, 20, 36, 42

Offset

1,7

Links

Table of n, a(n) for n=1..76.

Hart, George W., Uniform Polyhedra.

Maeder, Roman E., Uniform Polyhedra.

Eric Weisstein's World of Mathematics, Uniform Polyhedron.

Formula

After 124th term, a(n) equals A055684(n-2) + 1 for n odd and A055684(n-2) + A055684(n/2-1) + A128115(n/2-1) + 2 for n even.

Example

a(20)=12 because there are the icosahedron, the small cubicuboctahedron, the great cubicuboctahedron, the cubitruncated cuboctahedron, the great icosahedron, the octadecagonal prism, two octadecagrammic (18/5 and 18/7) prisms, the enneagonal antiprism, two enneagrammic (9/2 and 9/4) antiprisms and the enneagrammic crossed antiprism.

Crossrefs

Cf. A128113, A128114.

Sequence in context: A079108 A165605 A230194 * A122669 A071942 A289189

Adjacent sequences: A128109 A128110 A128111 * A128113 A128114 A128115

Keyword

nonn

Author

Paulo de A. Sachs (sachs6(AT)yahoo.de), Feb 15 2007, corrected Feb 15 2007

Status

approved