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a(n) = 9*n^2 - 11*n + 3.
2

%I #12 Mar 10 2024 03:18:32

%S 1,17,51,103,173,261,367,491,633,793,971,1167,1381,1613,1863,2131,

%T 2417,2721,3043,3383,3741,4117,4511,4923,5353,5801,6267,6751,7253,

%U 7773,8311,8867,9441,10033,10643,11271,11917,12581,13263,13963,14681,15417,16171,16943

%N a(n) = 9*n^2 - 11*n + 3.

%C Central terms of triangle A214604.

%H G. C. Greubel, <a href="/A214660/b214660.txt">Table of n, a(n) for n = 1..1000</a>

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

%F G.f.: (1+14*x+3*x^2)/(1-x)^3. - _Harvey P. Dale_, Aug 29 2021

%F E.g.f.: -3 + (3 - 2*x + 9*x^2)*exp(x). - _G. C. Greubel_, Mar 09 2024

%t Table[9n^2-11n+3,{n,60}] (* or *) LinearRecurrence[{3,-3,1},{1,17,51},60] (* _Harvey P. Dale_, Aug 29 2021 *)

%o (Haskell)

%o a214660 n = (9 * n - 11) * n + 3

%o (PARI) a(n)=9*n^2-11*n+3 \\ _Charles R Greathouse IV_, Jun 17 2017

%o (Magma) [9*n^2-11*n+3: n in [1..60]]; // _G. C. Greubel_, Mar 09 2024

%o (SageMath) [9*n^2-11*n+3 for n in range(1,61)] # _G. C. Greubel_, Mar 09 2024

%Y Cf. A214604, A214675.

%K nonn,easy

%O 1,2

%A _Reinhard Zumkeller_, Jul 25 2012