0

What is the geometric 2-dimensional shape of the following sequence:

{1, 4, 8, 13, 20, 27, 36, 47, 58, 70, 83, 99, 116, 132, 151, 170, 192, 214, 238, 262, 287, 316, 343, 373, 405, 435, 468, 502, 539, 576, 613, 654, 693,...}

It is generated by this program:

(*Mathematica program start*)
nn = 32;
a4 = Table[
  Total[Accumulate[
    Sum[Table[
      If[And[If[n^2 + k^2 <= r^2, If[n >= k, 1, 0], 0] == 1, 
        If[(n + 1)^2 + (k + 1)^2 <= r^2, If[n >= k, 1, 0], 0] == 0], 
       1, 0], {k, 0, r}], {n, 0, r}]]], {r, 0, 
   nn}]
(*Mathematica program end*)

This question is the first step that needs to be solved in order to answer this other question:

What is the shape of the set of integer sided acute triangles with largest side n?

I have tried programming this in a spreadsheet but I am not getting anywhere.

Trying to break down the question further: This arrayplot is closely related to the 14-th term of the sequence above:

r = 14;
ArrayPlot[
 Table[Table[
   If[And[If[n^2 + k^2 <= r^2, If[n >= k, 1, 0], 0] == 1, 
     If[(n + 1)^2 + (k + 1)^2 <= r^2, If[n >= k, 1, 0], 0] == 0], 1, 
    0], {k, 0, r}], {n, 0, r}]]

14-th term

Community
  • 1
Mats Granvik
  • 7,396
  • Did you try Wolfram Alpha? It sounds like an answer would roughly be a copy-paste job from this page. What is your actual question? – Mario Carneiro Apr 06 '15 at 12:53
  • @MarioCarneiro Thanks for the comment. But I am not looking for the graph of the sequence. I want to know which geometric area in a point lattice that the shape encloses. Analogous to the way a circle encloses points in Gauss Circle Problem: http://mathworld.wolfram.com/GausssCircleProblem.html. – Mats Granvik Apr 06 '15 at 12:57

0 Answers0