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A192675
Floor-Sqrt transform of large Fine numbers (A000957).
0
0, 1, 0, 1, 1, 2, 4, 7, 13, 24, 46, 85, 160, 301, 570, 1083, 2064, 3943, 7553, 14501, 27901, 53784, 103859, 200867, 389044, 754502, 1465037, 2847895, 5541797, 10794360, 21044286, 41061688, 80182834, 156692019, 306417804, 599604941, 1174044166, 2300154199, 4508885393, 8843184248
OFFSET
0,6
FORMULA
a(n) = floor(sqrt(Fine(n))).
MAPLE
b:= proc(n) option remember; `if`(n<3, n*(2-n),
((7*n-12)*b(n-1)+(4*n-6)*b(n-2))/(2*n))
end:
a:= n-> floor(sqrt(b(n))):
seq(a(n), n=0..40); # Alois P. Heinz, Apr 26 2023
MATHEMATICA
FSFromSeries[f_, x_, n_] := Map[Floor[Sqrt[#]]&, CoefficientList[Series[f, {x, 0, n}], x]]
FSFromSeries[(1+2x-Sqrt[1-4x])/(2x(2+x)), x, 100]
PROG
(Python)
from math import isqrt
from itertools import count, islice
def A192675_gen(): # generator of terms
yield from (0, 1, 0)
a, c = 0, 1
for n in count(1):
yield isqrt(a:=(c:=c*((n<<2)+2)//(n+2))-a>>1)
A192675_list = list(islice(A192675_gen(), 20)) # Chai Wah Wu, Apr 26 2023
CROSSREFS
Cf. A000957.
Sequence in context: A260668 A371789 A018184 * A018185 A191526 A005255
KEYWORD
nonn
AUTHOR
Emanuele Munarini, Jul 07 2011
EXTENSIONS
a(0) inserted by Chai Wah Wu, Apr 26 2023
STATUS
approved