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A194154 All possible numbers of whole squares which can be contained inside a square drawn with all of its vertices on lattice points. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 18 13:51 EDT 2021. Contains 347527 sequences. (Running on oeis4.)