A357303 Records in the numbers of representations of k^2 as x^2 - x*y + y^2, x > 2*y >= 0, corresponding to the numbers of grid points with squared radius A357302(n)^2 in an angular sector 0 <= phi < Pi/6 of the triangular lattice.

1, 2, 3, 5, 8, 14, 23, 41, 68, 122, 203, 365, 608, 851, 1094, 1823, 2552, 3281, 5468, 7655, 9842, 16403, 22964, 29525, 49208, 68891, 82013, 88574, 114818, 147623, 206672, 246038, 265721

Offset: 1

Author

Hugo Pfoertner, Sep 25 2022

Keywords

• nonn
• more

Comments

The total number of possible representations of A357302(n)^2 = x^2 + x*y + y^2 with integers x,y is 12*a(n) - 6.

Examples

			See A357302.
		

Crossrefs

Cf. A002324, A003136, A004016, A230655, A357302.

A246360 seems to be a subsequence.

Cf. A087503.

Programs

Mathematica

records[n_] := Module[{ri = n, m = 0, rcs = {}, len}, len = Length[ri];
   While[len > 0, If[First[ri] > m, m = First[ri]; AppendTo[rcs, m]];
    ri = Rest[ri]; len--]; rcs]; (* after Harvey P. Dale in A336679 *)
records[Table[
  Length[FindInstance[
    x^2 - x*y + y^2 == k^2 && x > 2*y && y >= 0, {x, y}, Integers,
    1000]], {k, 0, 2000}]]