A235702 Fixed points of A001175 (Pisano periods).

1, 24, 120, 600, 3000, 15000, 75000, 375000, 1875000, 9375000, 46875000, 234375000, 1171875000, 5859375000, 29296875000, 146484375000, 732421875000, 3662109375000, 18310546875000, 91552734375000, 457763671875000, 2288818359375000, 11444091796875000

Offset: 1

Author

Reinhard Zumkeller, Jan 15 2014

Keywords

• nonn
• easy

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..1430
• Shaoshi Chen, Hanqian Fang, Sergey Kitaev, and Candice X.T. Zhang, Patterns in Multi-dimensional Permutations, arXiv:2411.02897 [math.CO], 2024. See pp. 2, 26.
• J. D. Fulton and W. L. Morris, On arithmetical functions related to the Fibonacci numbers, Acta Arithmetica, 16 (1969), 105-110.
• Wikipedia, Pisano period
• Index entries for linear recurrences with constant coefficients, signature (5).

Crossrefs

Cf. A001175, A001178, A008606, A000351.

Programs

Haskell

a235702 n = if n == 1 then 1 else 24 * 5 ^ (n - 2)
a235702_list = 1 : iterate (* 5) 24

Mathematica

LinearRecurrence[{5},{1,24},30] (* or *) Join[{1},NestList[5#&,24,30]] (* Harvey P. Dale, May 07 2017 *)

PARI

Vec(-x*(19*x+1)/(5*x-1) + O(x^100)) \\ Colin Barker, Jan 16 2014

Formula

A001175(a(n)) = a(n); A001178(a(n)) = 0.

From Colin Barker, Jan 16 2014: (Start)

a(n) = 24*5^(n-2) for n > 1.

a(n) = 5*a(n-1) for n > 2.

G.f.: -x*(19*x+1) / (5*x-1). (End)

E.g.f.: (24*(exp(5*x) - 1) - 95*x)/25. - Stefano Spezia, Nov 09 2024