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a(n) = 49*n^2 - 2*n.
5

%I #30 Sep 17 2022 08:47:47

%S 47,192,435,776,1215,1752,2387,3120,3951,4880,5907,7032,8255,9576,

%T 10995,12512,14127,15840,17651,19560,21567,23672,25875,28176,30575,

%U 33072,35667,38360,41151,44040,47027,50112,53295,56576,59955,63432,67007

%N a(n) = 49*n^2 - 2*n.

%C The identity (4802*n^2-196*n+1)^2-(49*n^2-2*n)*(686*n-14)^2=1 can be written as A157364(n)^2-a(n)*A157363(n)^2=1.

%C The continued fraction expansion of sqrt(4*a(n)) is [14n-1; {1, 2, 2, 7n-1, 2, 2, 1, 28n-2}]. - _Magus K. Chu_, Sep 17 2022

%H Vincenzo Librandi, <a href="/A157362/b157362.txt">Table of n, a(n) for n = 1..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) = 3*a(n-1) -3*a(n-2) +a(n-3).

%F G.f.: x*(47+51*x)/(1-x)^3.

%F E.g.f. x*(47 + 49*x)*exp(x). - _G. C. Greubel_, Feb 02 2018

%t LinearRecurrence[{3,-3,1},{47,192,435},50]

%t Table[49n^2-2n,{n,40}] (* _Harvey P. Dale_, Jun 10 2019 *)

%o (Magma) I:=[47, 192, 435]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];

%o (PARI) a(n)=49*n^2-2*n \\ _Charles R Greathouse IV_, Dec 23 2011

%Y Cf. A157363, A157364.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Feb 28 2009