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 A195027 #40 Dec 30 2024 09:59:32
%S A195027 0,24,76,156,264,400,564,756,976,1224,1500,1804,2136,2496,2884,3300,
%T A195027 3744,4216,4716,5244,5800,6384,6996,7636,8304,9000,9724,10476,11256,
%U A195027 12064,12900,13764,14656,15576,16524,17500,18504,19536,20596,21684,22800,23944,25116,26316
%N A195027 a(n) = 2*n*(7*n + 5).
%C A195027 Sequence found by reading the line from 0, in the direction 0, 24, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. Semi-axis opposite to A195023 in the same square spiral, which is related to the primitive Pythagorean triple [3, 4, 5].
%H A195027 Vincenzo Librandi, <a href="/A195027/b195027.txt">Table of n, a(n) for n = 0..10000</a>
%H A195027 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A195027 a(n) = 14*n^2 + 10*n.
%F A195027 a(n) = 4*A179986(n). - _Bruno Berselli_, Oct 13 2011
%F A195027 G.f.: 4*x*(6+x)/(1-x)^3. - _Colin Barker_, Jan 09 2012
%F A195027 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=0, a(1)=24, a(2)=76. - _Harvey P. Dale_, Jul 24 2012
%F A195027 E.g.f.: 2*exp(x)*x*(12 + 7*x). - _Elmo R. Oliveira_, Dec 30 2024
%t A195027 Table[2n(7n+5),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,24,76},50] (* _Harvey P. Dale_, Jul 24 2012 *)
%o A195027 (Magma) [14*n^2 +10*n: n in [0..50]]; // _Vincenzo Librandi_, Oct 14 2011
%o A195027 (PARI) a(n)=2*n*(7*n+5) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A195027 Cf. A144555, A152760, A179986, A195019, A195020, A195021, A195023, A195024, A195025, A195026, A195320.
%Y A195027 Cf. A185019, A193053, A198017.
%K A195027 nonn,easy
%O A195027 0,2
%A A195027 _Omar E. Pol_, Oct 13 2011