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 A242658 #41 Feb 16 2025 08:33:22
%S A242658 2,2,8,20,38,62,92,128,170,218,272,332,398,470,548,632,722,818,920,
%T A242658 1028,1142,1262,1388,1520,1658,1802,1952,2108,2270,2438,2612,2792,
%U A242658 2978,3170,3368,3572,3782,3998,4220,4448,4682,4922,5168,5420,5678,5942,6212,6488,6770,7058,7352
%N A242658 a(n) = 3*n^2 - 3*n + 2.
%C A242658 An exercise in Smith (1950), my secondary school algebra book.
%C A242658 For n > 0, also the number of (not necessarily maximal) cliques in the (n-1)-triangular grid graph. - _Eric W. Weisstein_, Nov 29 2017
%D A242658 C. Smith, A Treatise on Algebra, Macmillan, London, 5th ed., 1950, p. 429, Example 2(i).
%H A242658 Vincenzo Librandi, <a href="/A242658/b242658.txt">Table of n, a(n) for n = 0..1000</a>
%H A242658 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Clique.html">Clique</a>
%H A242658 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TriangularGridGraph.html">Triangular Grid Graph</a>
%H A242658 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A242658 From _Chai Wah Wu_, May 30 2016: (Start)
%F A242658 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
%F A242658 G.f.: 2*(-4*x^2 + 2*x - 1)/(x - 1)^3. (End)
%F A242658 E.g.f.: exp(x)*(2 + 3*x^2). - _Stefano Spezia_, Dec 27 2021
%F A242658 a(n) = A002378(n) + A002378(n-1) + A002378(n-2). - _Peter Bala_, Jun 11 2024
%t A242658 Table[3 n^2 - 3 n + 2, {n, 0, 100}] (* _Vincenzo Librandi_, Sep 05 2016 *)
%t A242658 LinearRecurrence[{3, -3, 1}, {2, 8, 20}, {0, 20}] (* _Eric W. Weisstein_, Nov 29 2017 *)
%t A242658 CoefficientList[Series[-2 (1 - 2 x + 4 x^2)/(-1 + x)^3, {x, 0, 20}], x] (* _Eric W. Weisstein_, Nov 29 2017 *)
%o A242658 (Magma) [3*n^2 - 3*n + 2: n in [0..70]]; // _Vincenzo Librandi_, Sep 05 2016
%o A242658 (PARI) a(n) = 3*n^2-3*n+2 \\ _Altug Alkan_, Sep 05 2016
%Y A242658 A077588 is the same except for the initial term.
%Y A242658 Cf. A002378, A242659.
%K A242658 nonn,easy
%O A242658 0,1
%A A242658 _N. J. A. Sloane_, May 30 2014