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%I #8 May 27 2018 10:43:27
%S 1,32,7,12,17,46,3042,319,835,2188,5730,375131,39282,102845,269253,
%T 704915,46137317,4831563,12649196,33116027,86698886,5674515856,
%U 594243013,1555748409,4073002214,10663258234,697919312217,73087059232
%N Maximum element in the continued fraction expansion of F(n+1)^5/F(n)^5 where F=A000045.
%F 5*a(5n)=F(10n+1)-(-1)^n-5; 5*a(5n+1)=F(10n+3)-2*(-1)^n-5; a(5n+2)=5*F(10n+5)+7*(-1)^n-1; 5a(5n+3)=F(10n+7)-3*(-1)^n-5; 5a(5n+4)=F(10n+9)+(-1)^n-5.
%F Empirical g.f.: x*(6*x^19 -5*x^17 +x^16 -x^15 -732*x^14 -x^13 +593*x^12 -107*x^11 +118*x^10 -743*x^9 +94*x^8 -327*x^7 +786*x^6 +93*x^5 -5*x^4 -5*x^3 +25*x^2 -31*x -1) / ((x -1) * (x +1) * (x^2 -3*x +1) * (x^4 -x^3 +x^2 -x +1) * (x^4 -x^3 +6*x^2 +4*x +1) * (x^4 +4*x^3 +6*x^2 -x +1)). - _Colin Barker_, Jun 17 2013
%t Max[ContinuedFraction[#[[2]]/#[[1]]]]&/@Partition[Fibonacci[ Range[ 30]]^5,2,1] (* _Harvey P. Dale_, May 27 2018 *)
%o (PARI) a(n)=vecmax(contfrac(fibonacci(n+1)^5/fibonacci(n)^5))
%Y Cf. A113500.
%K nonn
%O 1,2
%A _Benoit Cloitre_, Jan 11 2006
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