

A190568


Number of squares between powers of 2, floor(sqrt(2^(n+1)))  floor(sqrt(2^n))


2



1, 0, 1, 0, 2, 1, 3, 3, 5, 6, 10, 13, 19, 26, 38, 53, 75, 106, 150, 212, 300, 424, 600, 848, 1200, 1696, 2400, 3393, 4799, 6786, 9598, 13572, 19196, 27145, 38391, 54291, 76781, 108583, 153561, 217167, 307121, 434334, 614242, 868668, 1228484, 1737337, 2456967, 3474675, 4913933
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OFFSET

1,5


COMMENTS

A190568(n)/A190568(n1) converges to sqrt(2) (A002193).  John W. Nicholson, May 15 2011


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..6646


FORMULA

a(n) = floor(sqrt(2^(n+1)))  floor(sqrt(2^n)).


EXAMPLE

Between 2^6=64 and 2^(6+1)=128 are the squares 81=9^2, 100=10^2, 121=11^2, so a(n)=3


MATHEMATICA

Table[Floor[Sqrt[2^(n + 1)]]  Floor[Sqrt[2^n]], {n, 1, 120}] (* G. C. Greubel, Aug 19 2018 *)


PROG

(PARI) a(n)=sqrtint(1<<(n+1))sqrtint(1<<n) \\ Charles R Greathouse IV, May 12, 2011
(MAGMA) [Floor(Sqrt(2^(n+1)))  Floor(Sqrt(2^n)): n in [1..50]]; // G. C. Greubel, Aug 19 2018


CROSSREFS

Cf. A000079, A000290
Sequence in context: A173510 A238785 A241389 * A059876 A095354 A132883
Adjacent sequences: A190565 A190566 A190567 * A190569 A190570 A190571


KEYWORD

nonn,easy


AUTHOR

John W. Nicholson, May 12 2011


EXTENSIONS

Definition corrected by Bruno Berselli, May 13 2011


STATUS

approved



