A387001 Number of vertices in the diagram called "symmetric representation of sigma(n)" where its "parts" or polygons are dissected into unit squares (see the example).

4, 8, 11, 16, 17, 25, 23, 32, 32, 39, 35, 53, 41, 53, 55, 64, 53, 76, 59, 83, 75, 81, 71, 109, 82, 95, 95, 113, 89, 133, 95, 128, 115, 123, 119, 164, 113, 137, 135, 171, 125, 181, 131, 173, 169, 165, 143, 221, 156, 194, 175, 203, 161, 229, 183, 233, 195, 207, 179, 289, 185, 221, 231, 256

Offset: 1

Author

Omar E. Pol, Aug 14 2025

Keywords

• nonn
• new

Comments

Consider here that in the diagram every edge has length 1 and every face is a unit square.

The number of faces is A000203(n).

The number of edges is 2*A155085(n).

The number of edges with the same orientation is A155085(n).

Examples

			For n = 5 the diagram is as shown below:
   _ _ _
  |_|_|_|
        |_ _
          |_|
          |_|
          |_|
.
The number of vertices is a(5) = 17.
The number of faces is A000203(5) = 6.
The number of edges is 2*A155085(5) = 2*11 = 22.
The number of edges with the same orientation is A155085(5) = 11.
		

Links

• Omar E. Pol, Illustration of initial terms of A000203 in a concave polyhedron (n = 1..16)

Crossrefs

Cf. A000203, A005408, A155085, A224880, A237270, A237271, A237593.

Formula

a(n) = A000203(n) + A005408(n).

a(n) = 2*A155085(n) - A000203(n) + 1. (Euler's formula: V = E - F + 1).

a(n) = A224880(n) + 1.