A235337 - OEIS

%I #17 Nov 30 2019 01:33:48

%S 1,5,13,13,25,41,41,61,85,113,113,145,181,181,221,265,313,313,365,421,

%T 421,481,545,545,613,685,761,761,841,925,925,1013,1105,1201,1201,1301,

%U 1405,1405,1513,1625,1625,1741,1861,1985,1985,2113,2245,2245,2381,2521

%N Number of integer lattice points inside the square ABCD with side length n>0 with A(-n*sqrt(2)/2| 0), B(n*sqrt(2)/2| 0), C(0| n*sqrt(2)/2) and D(-n*sqrt(2)/2| 0).

%H Reiner Moewald and Vincenzo Librandi, <a href="/A235337/b235337.txt">Table of n, a(n) for n = 1..1000</a> (first 500 terms from Reiner Moewald)

%F a(n) := 2*z^2-2*z+1, where z = ceiling(n*sqrt(2)/2). - _Giovanni Resta_, Jan 10 2014

%t a[n_] := Block[{z = Ceiling[Sqrt[2]*n/2]}, 1-2*z+2*z^2]; Array[a,50] (* _Giovanni Resta_, Jan 10 2014 *)

%K nonn

%O 1,2

%A _Reiner Moewald_, Jan 06 2014