cp's OEIS Frontend

A192675 Floor-Sqrt transform of large Fine numbers (A000957).

%I A192675 #12 Apr 26 2023 18:27:42
%S A192675 0,1,0,1,1,2,4,7,13,24,46,85,160,301,570,1083,2064,3943,7553,14501,
%T A192675 27901,53784,103859,200867,389044,754502,1465037,2847895,5541797,
%U A192675 10794360,21044286,41061688,80182834,156692019,306417804,599604941,1174044166,2300154199,4508885393,8843184248
%N A192675 Floor-Sqrt transform of large Fine numbers (A000957).
%F A192675 a(n) = floor(sqrt(Fine(n))).
%p A192675 b:= proc(n) option remember; `if`(n<3, n*(2-n),
%p A192675       ((7*n-12)*b(n-1)+(4*n-6)*b(n-2))/(2*n))
%p A192675     end:
%p A192675 a:= n-> floor(sqrt(b(n))):
%p A192675 seq(a(n), n=0..40);  # _Alois P. Heinz_, Apr 26 2023
%t A192675 FSFromSeries[f_,x_,n_] := Map[Floor[Sqrt[#]]&,CoefficientList[Series[f,{x,0,n}],x]]
%t A192675 FSFromSeries[(1+2x-Sqrt[1-4x])/(2x(2+x)),x,100]
%o A192675 (Python)
%o A192675 from math import isqrt
%o A192675 from itertools import count, islice
%o A192675 def A192675_gen(): # generator of terms
%o A192675     yield from (0,1,0)
%o A192675     a, c = 0, 1
%o A192675     for n in count(1):
%o A192675         yield isqrt(a:=(c:=c*((n<<2)+2)//(n+2))-a>>1)
%o A192675 A192675_list = list(islice(A192675_gen(),20)) # _Chai Wah Wu_, Apr 26 2023
%Y A192675 Cf. A000957.
%K A192675 nonn
%O A192675 0,6
%A A192675 _Emanuele Munarini_, Jul 07 2011
%E A192675 a(0) inserted by _Chai Wah Wu_, Apr 26 2023