

A309945


a(n) = floor(n  sqrt(2*n1)).


1



0, 0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 7, 8, 8, 9, 10, 11, 12, 12, 13, 14, 15, 16, 17, 18, 18, 19, 20, 21, 22, 23, 24, 24, 25, 26, 27, 28, 29, 30, 31, 32, 32, 33, 34, 35, 36, 37, 38, 39, 40, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 60
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OFFSET

1,5


COMMENTS

The subsequence consisting of numbers that appear twice is A007590.
Sequence as triangle:
0;
0;
0; 1, 2;
2, 3, 4;
4, 5, 6, 7, 8;
8, 9, 10, 11, 12;
12, 13, 14, 15, 16, 17, 18;
18, 19, 20, 21, 22, 23, 24;
...
a(1) = 0; for n > 1, a(n) is the number of squares strictly between 2*n  2 and n^2.


LINKS

Table of n, a(n) for n = 1..999


FORMULA

a(n) = n1floor(sqrt(2*n2)).  Wesley Ivan Hurt, Dec 03 2020


EXAMPLE

For n = 3, 2*n  2 = 4, n^2 = 9, no square numbers strictly between 4 and 9, a(3) = 0.
For n=5, 2*n  2 = 8, n^2 = 25, two square numbers (9, 16) strictly between 8 and 25, a(5) = 2.


MATHEMATICA

Table[Floor[n(2*n1)^(1/2)], {n, 73}] (* Stefano Spezia, Aug 24 2019 *)


PROG

(PARI) a(n) = floor(n  sqrt(2*n1)); \\ Jinyuan Wang, Aug 26 2019
(Python)
from math import isqrt
def A309945(n): return (m:=n1)isqrt(m<<1) # Chai Wah Wu, Aug 04 2022


CROSSREFS

Cf. A007590, A080476, A016813.
Sequence in context: A122797 A281957 A286389 * A103354 A127038 A175268
Adjacent sequences: A309942 A309943 A309944 * A309946 A309947 A309948


KEYWORD

nonn


AUTHOR

Zhandos Mambetaliyev, Aug 24 2019


STATUS

approved



