A374622 Maximum number of vertices of a chordal ring mixed graph CRM(N,c) with diameter n.

8, 10, 18, 16, 32, 34, 50, 44, 72, 74, 98, 88, 128, 130, 162, 148, 200, 202, 242, 224, 288, 290, 338, 316, 392, 394, 450, 424, 512, 514, 578, 548, 648, 650, 722, 688, 800, 802, 882, 844, 968, 970, 1058, 1016, 1152, 1154

Offset: 3

Author

Miquel A. Fiol, Jul 14 2024

Keywords

• nonn

Examples

			For n = 9, the maximum number of vertices a(9) = 50 is attained by the chordal ring mixed graph CRM(50,9).
		

Links

• C. Dalfó, G. Erskine, G. Exoo, M. A. Fiol, and J. Tuite, On bipartite (1, 1, k)-mixed graphs, (2024).

Crossrefs

Cf. A371396.

Formula

If n is odd, a(n) = (n+1)^2/2.

Conjecture: If n is even, n=0 mod 4, a(n) = n^2/2+2;

If n (> 2) is even, n=2 mod 4, a(n) = n*(n/2 - 1) + 4.

Conjectured g.f.: 2*(1 + x + 2*x^2 + x^3 + 2*x^4 - 3*x^5 + 4*x^6 - x^7 + x^8)/((1 - x)^3*(1 + x + x^2 + x^3)^2). - Stefano Spezia, Jul 14 2024