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A235702 Fixed points of A001175 (Pisano periods).

%I A235702 #25 Nov 10 2024 08:58:02
%S A235702 1,24,120,600,3000,15000,75000,375000,1875000,9375000,46875000,
%T A235702 234375000,1171875000,5859375000,29296875000,146484375000,
%U A235702 732421875000,3662109375000,18310546875000,91552734375000,457763671875000,2288818359375000,11444091796875000
%N A235702 Fixed points of A001175 (Pisano periods).
%H A235702 Michael De Vlieger, <a href="/A235702/b235702.txt">Table of n, a(n) for n = 1..1430</a>
%H A235702 Shaoshi Chen, Hanqian Fang, Sergey Kitaev, and Candice X.T. Zhang, <a href="https://arxiv.org/abs/2411.02897">Patterns in Multi-dimensional Permutations</a>, arXiv:2411.02897 [math.CO], 2024. See pp. 2, 26.
%H A235702 J. D. Fulton and W. L. Morris, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa16/aa1621.pdf">On arithmetical functions related to the Fibonacci numbers</a>, Acta Arithmetica, 16 (1969), 105-110.
%H A235702 Wikipedia, <a href="http://en.wikipedia.org/wiki/Pisano_period">Pisano period</a>
%H A235702 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (5).
%F A235702 A001175(a(n)) = a(n); A001178(a(n)) = 0.
%F A235702 From _Colin Barker_, Jan 16 2014: (Start)
%F A235702 a(n) = 24*5^(n-2) for n > 1.
%F A235702 a(n) = 5*a(n-1) for n > 2.
%F A235702 G.f.: -x*(19*x+1) / (5*x-1). (End)
%F A235702 E.g.f.: (24*(exp(5*x) - 1) - 95*x)/25. - _Stefano Spezia_, Nov 09 2024
%t A235702 LinearRecurrence[{5},{1,24},30] (* or *) Join[{1},NestList[5#&,24,30]] (* _Harvey P. Dale_, May 07 2017 *)
%o A235702 (Haskell)
%o A235702 a235702 n = if n == 1 then 1 else 24 * 5 ^ (n - 2)
%o A235702 a235702_list = 1 : iterate (* 5) 24
%o A235702 (PARI)
%o A235702 Vec(-x*(19*x+1)/(5*x-1) + O(x^100)) \\ _Colin Barker_, Jan 16 2014
%Y A235702 Cf. A001175, A001178, A008606, A000351.
%K A235702 nonn,easy
%O A235702 1,2
%A A235702 _Reinhard Zumkeller_, Jan 15 2014