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%I #17 Mar 28 2021 12:10:35
%S 1,3,5,7,8,9,10,10,11,11,12,12,13,13,13,13,14,14,14,14,15,15,15,15,15,
%T 16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,18,
%U 18,18,18,19,19,19,19,19,19,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20
%N Number of Fibonacci numbers less than or equal to n^2.
%H David A. Corneth, <a href="/A137203/b137203.txt">Table of n, a(n) for n = 0..9999</a>
%H Planet Math, <a href="https://planetmath.org/listoffibonaccinumbers">list of Fibonacci numbers</a>.
%F a(n) = A108852(n^2). - _Michel Marcus_, Aug 03 2014
%e When n=1, the number of Fibonacci numbers less than or equal to 1 is 3.
%e When n=2, the number of Fibonacci numbers less than or equal to 4 is 5.
%e When n=3, the number of Fibonacci numbers less than or equal to 9 is 7.
%e When n=4, the number of Fibonacci numbers less than or equal to 16 is 8.
%t fibPi[n_] := 1 + Floor[ Log[ GoldenRatio, 1 + n*Sqrt@ 5]]; Array[ fibPi[#^2] &, 80, 0] (* _Robert G. Wilson v_, Aug 03 2014 *)
%o (PARI) first(n) = { res = vector(n+1); fibs = List([0, 1]); i = 2; n2 = n^2; f = 1; while(f <= n2, listput(fibs, f); i++; f = fibonacci(i) ); for(i = 1, #fibs, res[ceil(sqrt(fibs[i]))+1]++ ); for(i = 2, #res, res[i]+=res[i-1]); res} \\ _David A. Corneth_, Mar 28 2021
%Y Cf. A000045, A108852.
%K nonn
%O 0,2
%A _Parthasarathy Nambi_, Apr 04 2008
%E Corrected and extended by _Robert G. Wilson v_, Aug 03 2014
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