A194154 - OEIS

%I #33 Mar 16 2016 22:12:23

%S 0,1,4,5,9,12,13,16,17,20,24,25,28,33,36,37,40,41,45,49,52,53,60,61,

%T 64,65,72,73,76,80,81,84,85,92,93,100,101,104,105,108,109,112,113,116,

%U 117,121,124,125,129,132,136,137,144,145,148,149,153,156,157,160,164,169

%N All possible numbers of whole squares which can be contained inside a square drawn with all of its vertices on lattice points.

%H Ray Chandler, <a href="/A194154/b194154.txt">Table of n, a(n) for n = 1..10000</a>

%H C. Foster, <a href="http://www.foster77.co.uk/Foster,%20Mathematical%20Gazette,%20Squares%20within%20Squares.pdf">Squares Within Squares</a>, Mathematical Gazette, 96(537), 96.47, 2012.

%H Eugen J. Ionascu, <a href="http://arxiv.org/abs/1508.03643">Ehrhart polynomial for lattice squares, cubes and hypercubes</a>, arXiv:1508.03643 [math.NT], 2015. (Cites A194154 but gives a different sequence, which is now A269741.)

%t nmax = 1000;

%t a1 = {};

%t a = 1;

%t While[

%t   2 (a - 1)^2 <= nmax,

%t   b = a;

%t   While[

%t    c = (a - 1)^2 + (b - 1)^2;

%t    c <= nmax,

%t    h = GCD[a, b];

%t    c += 2 (h - 1);

%t    If[c <= nmax, AppendTo[a1, c]];

%t    b++;

%t    ];

%t   a++;

%t   ];

%t a1 = Union[a1]

%t (* _Ray Chandler_, Jun 01 2015 *)

%Y Cf. A269741.

%K nonn

%O 1,3

%A _Colin Foster_, Aug 17 2011

%E Extended by _Ray Chandler_, Jun 01 2015