A057544 Maximum cycle length (orbit size) in the rotation permutation of n+2 side polygon triangularizations.

1, 1, 2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68

Offset: 0

Author

Antti Karttunen, Sep 07 2000

Keywords

• nonn
• easy

Comments

I.e., in permutations A057161 and A057162 (also A057503 and A057504), the longest cycle among all cycles between the (A014138(n-2)+1)-th and (A014138(n-1))-th terms.

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A057542, A057543, A057545.

Programs

PARI

a(n)=if(n>2,n+2,1) \\ Charles R Greathouse IV, Jun 20 2024

Formula

a(0)=1, a(1)=1, a(2)=2, a(n)=n+2.

From Chai Wah Wu, Jul 28 2022: (Start)

a(n) = 2*a(n-1) - a(n-2) for n > 4.

G.f.: (-2*x^4 + 2*x^3 + x^2 - x + 1)/(x - 1)^2. (End)

Extensions

More terms from Sean A. Irvine, Jun 13 2022