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A016982 a(n) = (7*n)^2.

%I A016982 #25 Nov 30 2024 00:35:19
%S A016982 0,49,196,441,784,1225,1764,2401,3136,3969,4900,5929,7056,8281,9604,
%T A016982 11025,12544,14161,15876,17689,19600,21609,23716,25921,28224,30625,
%U A016982 33124,35721,38416,41209,44100,47089,50176,53361,56644,60025,63504,67081,70756,74529,78400
%N A016982 a(n) = (7*n)^2.
%H A016982 Vincenzo Librandi, <a href="/A016982/b016982.txt">Table of n, a(n) for n = 0..1000</a>
%H A016982 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A016982 From _Amiram Eldar_, Jan 25 2021: (Start)
%F A016982 Sum_{n>=1} 1/a(n) = Pi^2/294.
%F A016982 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/588.
%F A016982 Product_{n>=1} (1 + 1/a(n)) = sinh(Pi/7)/(Pi/7).
%F A016982 Product_{n>=1} (1 - 1/a(n)) = sin(Pi/7)/(Pi/7). (End)
%F A016982 From _Elmo R. Oliveira_, Nov 29 2024: (Start)
%F A016982 G.f.: 49*x*(1 + x)/(1-x)^3.
%F A016982 E.g.f.: 49*x*(1 + x)*exp(x).
%F A016982 a(n) = 49*A000290(n) = A008589(n)^2 = A000290(A008589(n)).
%F A016982 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%o A016982 (Magma) [(7*n)^2: n in [0..50]]; // _Vincenzo Librandi_, May 21 2011
%o A016982 (PARI) a(n)=(7*n)^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A016982 Cf. A000290, A008589.
%K A016982 nonn,easy
%O A016982 0,2
%A A016982 _N. J. A. Sloane_