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%I #7 May 15 2023 17:23:48
%S -28,-27,-24,-19,-12,-3,8,21,36,53,72,93,116,141,168,197,228,261,296,
%T 333,372,413,456,501,548,597,648,701,756,813,872,933,996,1061,1128,
%U 1197,1268,1341,1416,1493,1572,1653,1736,1821,1908,1997,2088,2181,2276,2373
%N Integers n such that n+28 is a square.
%C Values x of nonzero solutions (x, y) to the Diophantine equation x^3+28*x^2 = y^2. Corresponding values y are in A155137.
%C Agrees with A155135 except for omission of zero after a(6) = 3.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = n^2-2*n-27.
%F G.f.: -(4-3*x)*(7-9*x)/(1-x)^3.
%e For n = -19, n+28 = 9 = 3^2 is a square; for n = -3, n+28 = 25 = 5^2 is a square; for n = 21, n+28 = 49 = 7^2 is a square.
%t Range[0,50]^2-28 (* or *) LinearRecurrence[{3,-3,1},{-28,-27,-24},50] (* _Harvey P. Dale_, May 15 2023 *)
%o (Magma) [ n: n in [ -30..2500] | IsSquare(n+28) ];
%o (PARI) a(n)=n^2-2*n-27 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A155135, A155138, A153642.
%K sign,easy
%O 1,1
%A _Klaus Brockhaus_, Jan 21 2009
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