A082532 a(n) = n^2 - 2*floor(n/sqrt(2))^2.

1, 2, 1, 8, 7, 4, 17, 14, 9, 2, 23, 16, 7, 34, 25, 14, 1, 36, 23, 8, 49, 34, 17, 64, 47, 28, 7, 62, 41, 18, 79, 56, 31, 4, 73, 46, 17, 92, 63, 32, 113, 82, 49, 14, 103, 68, 31, 126, 89, 50, 9, 112, 71, 28, 137, 94, 49, 2

Offset: 1

Author

Carmine Suriano, May 01 2003

Keywords

• easy
• nonn

Examples

			a(3)=1 since 3^2 - 2*floor(3/1.4142..)^2 = 9 - 2*2^2 = 9 - 8 = 1.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

a(n)=1 for n in A001541.

Programs

Magma

[n^2 - 2*Floor(n/Sqrt(2))^2: n in [1..50]]; // G. C. Greubel, Jan 27 2018

Maple

A049472 := proc(n) floor(n/sqrt(2)) ; end proc:
A082532 := proc(n) n^2-2*A049472(n)^2 ; end proc:
seq(A082532(n),n=1..80) ; # R. J. Mathar, Mar 28 2011

Mathematica

Table[n^2 - 2*Floor[n/Sqrt[2]]^2, {n, 1, 100}] (* G. C. Greubel, Jan 27 2018 *)

PARI

for(n=1,50, print1(n^2 - 2*floor(n/sqrt(2))^2, ", ")) \\ G. C. Greubel, Jan 27 2018

Formula

a(n) = n^2 - 2*(A049472(n))^2. - R. J. Mathar, Mar 28 2011