A354529 a(1) = 3, a(2) = 12 and a(n) = (3n^2+8n-2)/2 if n is even or = (3n^2+8n-5)/2, if n is odd, for n >= 3.

3, 12, 23, 39, 55, 77, 99, 127, 155, 189, 223, 263, 303, 349, 395, 447, 499, 557, 615, 679, 743, 813, 883, 959, 1035, 1117, 1199, 1287, 1375, 1469, 1563, 1663, 1763, 1869, 1975, 2087, 2199, 2317, 2435, 2559, 2683, 2813, 2943, 3079, 3215, 3357, 3499, 3647, 3795, 3949, 4103, 4263, 4423

Offset: 1

Author

Sela Fried, Aug 16 2022

Keywords

• nonn
• easy

Comments

The disorder number M(G) of a graph G is defined to be the maximal length of a walk along the edges of the graph, according to any ordering of its vertices.

Conjecture: a(n) = M(P_3 X P_n) where P_3 X P_n is the grid graph of size 3 X n.

Links

• Sela Fried, The disorder number of a graph, arXiv:2208.03788 [math.CO], 2022.
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Crossrefs

Cf. A047838, A028347, A179094, A354528.

Programs

Python

def A354529(n): return 9*n-6 if n<3 else n*(3*n+8)-2-3*(n&1)>>1 # Chai Wah Wu, Sep 11 2022

Formula

From Stefano Spezia, Aug 16 2022: (Start)

O.g.f.: x*(3 + 6*x - x^2 - x^3 - 2*x^4 + x^5)/((1 - x)^3*(1 + x)).

E.g.f.: ((3*x^2 + 11*x - 2)*cosh(x) + (3*x^2 + 11*x - 5)*sinh(x) - x^2 + 2)/2. (End)