A325300 a(n) is the number of faces of the stepped pyramid with n levels described in A245092.

6, 9, 15, 20, 24, 31, 35, 42, 49, 59, 63, 72, 76, 84, 95, 106, 110, 121, 125

Offset: 1

Author

Omar E. Pol, Apr 16 2019

Keywords

• nonn
• more

Comments

To calculate a(n) consider that levels greater than n do not exist.

The shape of the n-th level of the pyramid allows us to know if n is prime (see the Formula section).

For more information about the sequences that we can see in the pyramid see A262626.

Examples

			For n = 1 the first level of the stepped pyramid (starting from the top) is a cube, and a cube has six faces, so a(1) = 6.
		

Links

• Omar E. Pol, Perspective view of the pyramid (first 16 levels)

Crossrefs

Cf. A325301 (number of edges), A325302 (number of vertices).

Cf. A196020, A215848, A235791, A236104, A237270, A237271, A237591, A237593, A245092, A262626, A299692, A323645, A323648.

Formula

a(n) = A325301(n) - A325302(n) + 2 (Euler's formula).

a(n) = A323645(n) + 3.

a(n) = a(n-1) + 4 iff n is a prime > 3 (A215848).