cp's OEIS Frontend

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.

%I A354529 #33 Sep 11 2022 10:30:54
%S A354529 3,12,23,39,55,77,99,127,155,189,223,263,303,349,395,447,499,557,615,
%T A354529 679,743,813,883,959,1035,1117,1199,1287,1375,1469,1563,1663,1763,
%U A354529 1869,1975,2087,2199,2317,2435,2559,2683,2813,2943,3079,3215,3357,3499,3647,3795,3949,4103,4263,4423
%N 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.
%C A354529 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.
%C A354529 Conjecture: a(n) = M(P_3 X P_n) where P_3 X P_n is the grid graph of size 3 X n.
%H A354529 Sela Fried, <a href="https://arxiv.org/abs/2208.03788">The disorder number of a graph</a>, arXiv:2208.03788 [math.CO], 2022.
%H A354529 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A354529 From _Stefano Spezia_, Aug 16 2022: (Start)
%F A354529 O.g.f.: x*(3 + 6*x - x^2 - x^3 - 2*x^4 + x^5)/((1 - x)^3*(1 + x)).
%F A354529 E.g.f.: ((3*x^2 + 11*x - 2)*cosh(x) + (3*x^2 + 11*x - 5)*sinh(x) - x^2 + 2)/2. (End)
%o A354529 (Python)
%o A354529 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
%Y A354529 Cf. A047838, A028347, A179094, A354528.
%K A354529 nonn,easy
%O A354529 1,1
%A A354529 _Sela Fried_, Aug 16 2022