A386292 The maximum possible number of 9-cycles in an outerplanar graph on n vertices.

1, 5, 11, 23, 34, 52, 68, 94, 109, 131, 151, 181, 200, 226, 250, 284, 299, 321, 341, 371, 390, 416, 440, 474, 489, 511, 531, 561, 580, 606, 630, 664, 679, 701, 721, 751, 770, 796, 820, 854, 869, 891, 911, 941, 960, 986, 1010, 1044, 1059, 1081, 1101, 1131, 1150

Offset: 9

Author

Stephen Bartell, Jul 17 2025

Keywords

• nonn
• easy

Comments

Excluding the first 7 terms, the first differences are 8-periodic: 15, 22, 20, 30, 19, 26, 24, 34.

Links

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

Crossrefs

Cf. A385869, A386226.

Formula

a(n) ~ (95/4)*n.

G.f.: x^9*(8*x^15+8*x^14+8*x^13+8*x^12+18*x^11+14*x^10+18*x^9+14*x^8+26*x^7+16*x^6 + 18*x^5 + 11*x^4+12*x^3+6*x^2+4*x+1) / ((x+1)*(x^2+1)*(x^4+1)*(x-1)^2). - Alois P. Heinz, Jul 17 2025