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%I #26 Aug 20 2023 10:50:13
%S 1,2,5,18,65,218,693,2138,6497,19602,58949,177026,531297,1594154,
%T 4782773,14348682,43046465,129139874,387420165,1162261106,3486784001,
%U 10460352762,31381059125,94143178298,282429535905,847288608818
%N a(n) = 3^n - n^2.
%H Vincenzo Librandi, <a href="/A024025/b024025.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,10,-3).
%F G.f.: (1-4*x+5*x^2+2*x^3)/((1-3*x)*(1-x)^3). - _Vincenzo Librandi_, Oct 05 2014
%F a(n) = 6*a(n-1) -12*a(n-2) +10*a(n-3) -3*a(n-4) for n>3. - _Vincenzo Librandi_, Oct 05 2014
%F a(n) = A000244(n) - A000290(n). - _Michel Marcus_, Oct 05 2014
%F E.g.f.: exp(3*x) - x*(1+x)*exp(x). - _G. C. Greubel_, Aug 18 2023
%p A024025:=n->3^n-n^2: seq(A024025(n), n=0..50); # _Wesley Ivan Hurt_, Jan 11 2017
%t Table[3^n - n^2, {n, 0, 25}] (* or *) CoefficientList[Series[(1 - 4 x + 5 x^2 + 2 x^3)/((1 - 3 x) (1 - x)^3), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 05 2014 *)
%o (Magma) [3^n-n^2: n in [0..30]]; // _Vincenzo Librandi_, Jul 02 2011
%o (SageMath) [3^n-n^2 for n in range(31)] # _G. C. Greubel_, Aug 18 2023
%Y Cf. sequences of the form k^n-n^2: A024012 (k=2), this sequence (k=3), A024038 (k=4), A024051 (k=5), A024064 (k=6), A024077 (k=7), A024090 (k=8), A024103 (k=9), A024116 (k=10), A024129 (k=11), A024142 (k=12).
%Y Cf. A000244, A000290.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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