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

1,2

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).

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

Mathematica

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

Prog

(Haskell)
a235702 n = if n == 1 then 1 else 24 * 5 ^ (n - 2)
a235702_list = 1 : iterate (* 5) 24
(PARI)
Vec(-x*(19*x+1)/(5*x-1) + O(x^100)) \\ Colin Barker, Jan 16 2014

Crossrefs

Cf. A001175, A001178, A008606, A000351.

Sequence in context: A292979 A052760 A179720 * A052754 A050213 A124657

Adjacent sequences: A235699 A235700 A235701 * A235703 A235704 A235705

Keyword

nonn,easy,changed

Author

Reinhard Zumkeller, Jan 15 2014

Status

approved