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%I #32 Dec 31 2022 05:38:56
%S 2,2,8,20,38,62,92,128,170,218,272,332,398,470,548,632,722,818,920,
%T 1028,1142,1262,1388,1520,1658,1802,1952,2108,2270,2438,2612,2792,
%U 2978,3170,3368,3572,3782,3998,4220,4448,4682,4922,5168,5420,5678,5942,6212,6488,6770,7058,7352
%N a(n) = 3*n^2 - 3*n + 2.
%C An exercise in Smith (1950), my secondary school algebra book.
%C 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 C. Smith, A Treatise on Algebra, Macmillan, London, 5th ed., 1950, p. 429, Example 2(i).
%H Vincenzo Librandi, <a href="/A242658/b242658.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Clique.html">Clique</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TriangularGridGraph.html">Triangular Grid Graph</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F From _Chai Wah Wu_, May 30 2016: (Start)
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
%F G.f.: 2*(-4*x^2 + 2*x - 1)/(x - 1)^3. (End)
%F E.g.f.: exp(x)*(2 + 3*x^2). - _Stefano Spezia_, Dec 27 2021
%t Table[3 n^2 - 3 n + 2, {n, 0, 100}] (* _Vincenzo Librandi_, Sep 05 2016 *)
%t LinearRecurrence[{3, -3, 1}, {2, 8, 20}, {0, 20}] (* _Eric W. Weisstein_, Nov 29 2017 *)
%t CoefficientList[Series[-2 (1 - 2 x + 4 x^2)/(-1 + x)^3, {x, 0, 20}], x] (* _Eric W. Weisstein_, Nov 29 2017 *)
%o (Magma) [3*n^2 - 3*n + 2: n in [0..70]]; // _Vincenzo Librandi_, Sep 05 2016
%o (PARI) a(n) = 3*n^2-3*n+2 \\ _Altug Alkan_, Sep 05 2016
%Y A077588 is the same except for the initial term.
%Y Cf. A242659.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_, May 30 2014
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