A194154 All possible numbers of whole squares which can be contained inside a square drawn with all of its vertices on lattice points.

0, 1, 4, 5, 9, 12, 13, 16, 17, 20, 24, 25, 28, 33, 36, 37, 40, 41, 45, 49, 52, 53, 60, 61, 64, 65, 72, 73, 76, 80, 81, 84, 85, 92, 93, 100, 101, 104, 105, 108, 109, 112, 113, 116, 117, 121, 124, 125, 129, 132, 136, 137, 144, 145, 148, 149, 153, 156, 157, 160, 164, 169

Offset

1,3

Links

Ray Chandler, Table of n, a(n) for n = 1..10000

C. Foster, Squares Within Squares, Mathematical Gazette, 96(537), 96.47, 2012.

Eugen J. Ionascu, Ehrhart polynomial for lattice squares, cubes and hypercubes, arXiv:1508.03643 [math.NT], 2015. (Cites A194154 but gives a different sequence, which is now A269741.)

Mathematica

nmax = 1000;
a1 = {};
a = 1;
While[
  2 (a - 1)^2 <= nmax,
  b = a;
  While[
   c = (a - 1)^2 + (b - 1)^2;
   c <= nmax,
   h = GCD[a, b];
   c += 2 (h - 1);
   If[c <= nmax, AppendTo[a1, c]];
   b++;
   ];
  a++;
  ];
a1 = Union[a1]
(* Ray Chandler, Jun 01 2015 *)

Crossrefs

Cf. A269741.

Sequence in context: A341783 A319606 A230239 * A297291 A269741 A047610

Adjacent sequences: A194151 A194152 A194153 * A194155 A194156 A194157

Keyword

nonn

Author

Colin Foster, Aug 17 2011

Extensions

Extended by Ray Chandler, Jun 01 2015

Status

approved