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a(n) = 7*n^2 - 5*n + 1.
3

%I #19 Nov 16 2024 19:17:08

%S 1,3,19,49,93,151,223,309,409,523,651,793,949,1119,1303,1501,1713,

%T 1939,2179,2433,2701,2983,3279,3589,3913,4251,4603,4969,5349,5743,

%U 6151,6573,7009,7459,7923,8401,8893,9399,9919,10453,11001,11563,12139,12729,13333,13951

%N a(n) = 7*n^2 - 5*n + 1.

%H Reinhard Zumkeller, <a href="/A239449/b239449.txt">Table of n, a(n) for n = 0..10000</a>

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

%F a(n) = A239426(n)/A003215(n-1).

%F G.f.: (-1-13*x^2)/(x-1)^3. - _R. J. Mathar_, Mar 31 2014

%F From _Elmo R. Oliveira_, Nov 16 2024: (Start)

%F E.g.f.: exp(x)*(1 + 2*x + 7*x^2).

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

%t CoefficientList[Series[(1 + 13 x^2)/(1 - x)^3, {x, 0, 50}], x] (* _Vincenzo Librandi_, Apr 02 2014 *)

%o (Haskell)

%o a239449 n = (7 * n - 5) * n + 1

%o (Magma) [7*n^2-5*n+1: n in [0..50]]; // _Vincenzo Librandi_, Apr 02 2014

%o (PARI) a(n)=7*n^2-5*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. A003215, A239426.

%K nonn,easy,changed

%O 0,2

%A _Reinhard Zumkeller_, Mar 19 2014