A385869 The maximum possible number of 7-cycles in an outerplanar graph on n vertices.

1, 4, 7, 12, 17, 24, 27, 32, 37, 44, 47, 52, 57, 64, 67, 72, 77, 84, 87, 92, 97, 104, 107, 112, 117, 124, 127, 132, 137, 144, 147, 152, 157, 164, 167, 172, 177, 184, 187, 192, 197, 204, 207, 212, 217, 224, 227, 232, 237, 244, 247, 252, 257, 264, 267, 272, 277, 284, 287, 292, 297

Offset: 7

Author

Stephen Bartell, Jul 10 2025

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Programs

Mathematica

Drop[CoefficientList[Series[x^7*(4*x^5+4*x^4+5*x^3+3*x^2+3*x+1)/((x+1)*(x^2+1)*(x-1)^2),{x,0,67}],x],7] (* James C. McMahon, Jul 16 2025 *)

Formula

For n >= 2, a(4n) = 20n-36, a(4n+1) = 20n-33, a(4n+2) = 20n-28, a(4n+3) = 20n-23.

For n >= 8, a(n) = 5n - 36 - 2sgn(mod(n,4))

Excluding a(7), the first differences are 4-periodic: 3,5,5,7,3,5,5,7,...

G.f.: x^7*(4*x^5+4*x^4+5*x^3+3*x^2+3*x+1)/((x+1)*(x^2+1)*(x-1)^2). - Alois P. Heinz, Jul 15 2025