cp's OEIS Frontend

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.

%I A357303 #9 Sep 27 2022 19:17:34
%S A357303 1,2,3,5,8,14,23,41,68,122,203,365,608,851,1094,1823,2552,3281,5468,
%T A357303 7655,9842,16403,22964,29525,49208,68891,82013,88574,114818,147623,
%U A357303 206672,246038,265721
%N 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.
%C A357303 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.
%e A357303 See A357302.
%t A357303 records[n_] := Module[{ri = n, m = 0, rcs = {}, len}, len = Length[ri];
%t A357303    While[len > 0, If[First[ri] > m, m = First[ri]; AppendTo[rcs, m]];
%t A357303     ri = Rest[ri]; len--]; rcs]; (* after _Harvey P. Dale_ in A336679 *)
%t A357303 records[Table[
%t A357303   Length[FindInstance[
%t A357303     x^2 - x*y + y^2 == k^2 && x > 2*y && y >= 0, {x, y}, Integers,
%t A357303     1000]], {k, 0, 2000}]]
%Y A357303 Cf. A002324, A003136, A004016, A230655, A357302.
%Y A357303 A246360 seems to be a subsequence.
%Y A357303 Cf. A087503.
%K A357303 nonn,more
%O A357303 1,2
%A A357303 _Hugo Pfoertner_, Sep 25 2022