A386226 The maximum possible number of 8-cycles in an outerplanar graph on n vertices.
1, 4, 10, 16, 27, 34, 44, 54, 69, 76, 86, 96, 111, 118, 128, 138, 153, 160, 170, 180, 195, 202, 212, 222, 237, 244, 254, 264, 279, 286, 296, 306, 321, 328, 338, 348, 363, 370, 380, 390, 405, 412, 422, 432, 447, 454, 464, 474, 489, 496, 506, 516, 531, 538, 548
Offset: 8
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
Programs
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Mathematica
Drop[CoefficientList[Series[x^8*(4*x^8+4*x^7+4*x^6+4*x^5+10*x^4+6*x^3+6*x^2+3*x+1)/((x+1)*(x^2+1)*(x-1)^2),{x,0,62}],x],8] (* James C. McMahon, Jul 16 2025 *)
Formula
a(n) = 10*n - 99 + 5*floor(n/4) - 3*floor((n+3)/4) for n >= 12.
a(n) ~ (21/2)*n.
G.f.: x^8*(4*x^8+4*x^7+4*x^6+4*x^5+10*x^4+6*x^3+6*x^2+3*x+1)/((x+1)*(x^2+1)*(x-1)^2). - Alois P. Heinz, Jul 15 2025
Comments