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A316621 Numbers of the form x^2 + 9*x*y + y^2, 0 <= x <= y. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A212017 A236171 A312838

Adjacent sequences:  A316618 A316619 A316620 * A316622 A316623 A316624

KEYWORD

nonn

AUTHOR

Gheorghe Coserea, Jul 29 2018

STATUS

approved

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Last modified August 18 15:00 EDT 2019. Contains 326106 sequences. (Running on oeis4.)