A316621 Numbers of the form x^2 + 9*x*y + y^2, 0 <= x <= y.

0, 1, 4, 9, 11, 16, 23, 25, 36, 37, 44, 49, 53, 64, 67, 71, 81, 91, 92, 99, 100, 113, 119, 121, 133, 137, 144, 148, 163, 169, 176, 179, 191, 196, 207, 212, 221, 225, 247, 253, 256, 268, 275, 284, 287, 289, 317, 323, 324, 331, 333, 361, 364, 368, 379, 389, 396, 400, 401, 407, 421, 427, 441, 443, 449

Offset

1,3

Comments

Discriminant 77.

In general, for k>=0 the positive part of the set S = {x^2 - k*x*y + y^2: x,y in Z} is given by the numbers of the form x^2 + k*x*y + y^2 with 0 <= x <= y natural numbers.

Links

Gheorghe Coserea, Table of n, a(n) for n = 1..100001

Prog

(PARI)
seq(M, k=9) = { \\ assume k >= 0
setintersect([1..M], setbinop((x, y)->x^2 + k*x*y + y^2, [0..1+sqrtint(M)]));
};
concat(0, seq(449))

Crossrefs

Numbers representable as x^2 + k*x*y + y^2 with 0 <= x <= y, for k=0..9: A001481(k=0), A003136(k=1), A000290(k=2), A031363(k=3), A084916(k=4), A243172(k=5), A242663(k=6), A243174(k=7), A243188(k=8), this sequence.

Sequence in context: A190547 A239435 A190559 * A336826 A212017 A362505

Adjacent sequences: A316618 A316619 A316620 * A316622 A316623 A316624

Keyword

nonn

Author

Gheorghe Coserea, Jul 29 2018

Status

approved