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

0,3

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

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

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

From G. C. Greubel, Dec 26 2025: (Start)

a(n) = n+2 - [n=0] - 2*[n=1] - 2*[n=2].

E.g.f.: (2 + x)*exp(x) - (1 + x)^2. (End)

Mathematica

Join[{1, 1, 2}, Range[5, 100]] (* G. C. Greubel, Dec 26 2025 *)

Prog

(PARI) a(n)=if(n>2, n+2, 1) \\ Charles R Greathouse IV, Jun 20 2024
(Magma) A057544:= func< n| n le 2 select Floor((n+2)/2) else n+2 >; // G. C. Greubel, Dec 26 2025
(SageMath)
def A057544(n): return ((n+2)//2) if n<3 else n+2 # G. C. Greubel, Dec 26 2025

Crossrefs

Cf. A014138, A057161, A057162, A057503, A057504, A057542, A057543, A057545.

Sequence in context: A198547 A120678 A078384 * A382445 A039239 A039182

Adjacent sequences: A057541 A057542 A057543 * A057545 A057546 A057547

Keyword

nonn,easy

Author

Antti Karttunen, Sep 07 2000

Extensions

More terms from Sean A. Irvine, Jun 13 2022

Status

approved