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a(n) = 3*n^2 - 7*n + 6.
4

%I #25 Aug 25 2022 05:04:14

%S 6,2,4,12,26,46,72,104,142,186,236,292,354,422,496,576,662,754,852,

%T 956,1066,1182,1304,1432,1566,1706,1852,2004,2162,2326,2496,2672,2854,

%U 3042,3236,3436,3642,3854,4072,4296,4526,4762,5004,5252,5506

%N a(n) = 3*n^2 - 7*n + 6.

%D Encyclopaedia Britannica, 1965 ed., Vol. 16 pp. 755-756.

%H G. C. Greubel, <a href="/A027599/b027599.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = a(n-1) + 6*n - 10 (with a(0)=6). - _Vincenzo Librandi_, Nov 19 2010

%F From _Colin Barker_, May 22 2012: (Start)

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

%F G.f.: 2*(3 - 8*x + 8*x^2)/(1 - x)^3. (End)

%F E.g.f.: (6 - 4*x + 3*x^2)*exp(x). - _G. C. Greubel_, Aug 24 2022

%t LinearRecurrence[{3,-3,1}, {6,2,4}, 61] (* _G. C. Greubel_, Aug 24 2022 *)

%o (PARI) a(n)=3*n^2-7*n+6 \\ _Charles R Greathouse IV_, Jun 17 2017

%o (Magma) [((6*n-7)^2+23)/12: n in [0..60]]; // _G. C. Greubel_, Aug 24 2022

%o (SageMath) [3*n^2-7*n+6 for n in (0..60)] # _G. C. Greubel_, Aug 24 2022

%Y Cf. A049450.

%K nonn,easy

%O 0,1

%A _Patrick De Geest_