cp's OEIS Frontend

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).

%I A387001 #31 Aug 20 2025 19:07:28
%S A387001 4,8,11,16,17,25,23,32,32,39,35,53,41,53,55,64,53,76,59,83,75,81,71,
%T A387001 109,82,95,95,113,89,133,95,128,115,123,119,164,113,137,135,171,125,
%U A387001 181,131,173,169,165,143,221,156,194,175,203,161,229,183,233,195,207,179,289,185,221,231,256
%N 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).
%C A387001 Consider here that in the diagram every edge has length 1 and every face is a unit square.
%C A387001 The number of faces is A000203(n).
%C A387001 The number of edges is 2*A155085(n).
%C A387001 The number of edges with the same orientation is A155085(n).
%H A387001 Omar E. Pol, <a href="/A000203/a000203_1.jpg">Illustration of initial terms of A000203 in a concave polyhedron (n = 1..16)</a>
%F A387001 a(n) = A000203(n) + A005408(n).
%F A387001 a(n) = 2*A155085(n) - A000203(n) + 1. (Euler's formula: V = E - F + 1).
%F A387001 a(n) = A224880(n) + 1.
%e A387001 For n = 5 the diagram is as shown below:
%e A387001    _ _ _
%e A387001   |_|_|_|
%e A387001         |_ _
%e A387001           |_|
%e A387001           |_|
%e A387001           |_|
%e A387001 .
%e A387001 The number of vertices is a(5) = 17.
%e A387001 The number of faces is A000203(5) = 6.
%e A387001 The number of edges is 2*A155085(5) = 2*11 = 22.
%e A387001 The number of edges with the same orientation is A155085(5) = 11.
%Y A387001 Cf. A000203, A005408, A155085, A224880, A237270, A237271, A237593.
%K A387001 nonn,new
%O A387001 1,1
%A A387001 _Omar E. Pol_, Aug 14 2025