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%I #20 Sep 08 2022 08:45:39
%S 0,13,52,117,208,325,468,637,832,1053,1300,1573,1872,2197,2548,2925,
%T 3328,3757,4212,4693,5200,5733,6292,6877,7488,8125,8788,9477,10192,
%U 10933,11700,12493,13312,14157,15028,15925,16848,17797,18772
%N 13 times the squares: a(n) = 13*n^2.
%H G. C. Greubel, <a href="/A152742/b152742.txt">Table of n, a(n) for n = 0..5000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 13*A000290(n).
%F a(n) = a(n-1) +26*n -13 (with a(0)=0). - _Vincenzo Librandi_, Nov 26 2010
%F a(0)=0, a(1)=13, a(2)=52, a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - _Harvey P. Dale_, Feb 18 2015
%F From _G. C. Greubel_, Sep 01 2018:(Start)
%F G.f.: 13*x*(1+x)/(1-x)^3.
%F E.g.f.: 13*(1+x)*exp(x). (End)
%F From _Amiram Eldar_, Feb 03 2021: (Start)
%F Sum_{n>=1} 1/a(n) = Pi^2/78.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/156.
%F Product_{n>=1} (1 + 1/a(n)) = sqrt(13)*sinh(Pi/sqrt(13))/Pi.
%F Product_{n>=1} (1 - 1/a(n)) = sqrt(13)*sin(Pi/sqrt(13))/Pi. (End)
%t 13*Range[0,40]^2 (* or *) LinearRecurrence[{3,-3,1},{0,13,52},40] (* _Harvey P. Dale_, Feb 18 2015 *)
%o (PARI) a(n)=13*n^2 \\ _Charles R Greathouse IV_, Oct 07 2015
%o (Magma) [13*n^2: n in [0..50]]; // _G. C. Greubel_, Sep 01 2018
%Y Cf. A000290, A135453.
%K easy,nonn
%O 0,2
%A _Omar E. Pol_, Dec 12 2008
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