This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A155136 #13 Oct 31 2024 21:58:11
%S A155136 -28,-27,-24,-19,-12,-3,8,21,36,53,72,93,116,141,168,197,228,261,296,
%T A155136 333,372,413,456,501,548,597,648,701,756,813,872,933,996,1061,1128,
%U A155136 1197,1268,1341,1416,1493,1572,1653,1736,1821,1908,1997,2088,2181,2276,2373
%N A155136 Integers k such that k + 28 is a square.
%C A155136 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 A155136 Agrees with A155135 except for omission of zero after a(6) = 3.
%H A155136 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A155136 a(n) = n^2 - 2*n - 27.
%F A155136 G.f.: -(4-3*x)*(7-9*x)/(1-x)^3.
%F A155136 From _Elmo R. Oliveira_, Oct 31 2024: (Start)
%F A155136 E.g.f.: exp(x)*(x^2 - x - 27) + 27.
%F A155136 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
%e A155136 For k = -19, k + 28 = 9 = 3^2 is a square.
%e A155136 For k = -3, k + 28 = 25 = 5^2 is a square.
%e A155136 For k = 21, k + 28 = 49 = 7^2 is a square.
%t A155136 Range[0,50]^2-28 (* or *) LinearRecurrence[{3,-3,1},{-28,-27,-24},50] (* _Harvey P. Dale_, May 15 2023 *)
%o A155136 (Magma) [ n: n in [ -30..2500] | IsSquare(n+28) ];
%o A155136 (PARI) a(n)=n^2-2*n-27 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A155136 Cf. A153642, A155135, A155137, A155138.
%K A155136 sign,easy
%O A155136 1,1
%A A155136 _Klaus Brockhaus_, Jan 21 2009