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%I #31 Sep 08 2022 08:45:41
%S 106846,244688,382530,520372,658214,796056,933898,1071740,1209582,
%T 1347424,1485266,1623108,1760950,1898792,2036634,2174476,2312318,
%U 2450160,2588002,2725844,2863686,3001528,3139370,3277212,3415054
%N a(n) = 137842*n - 30996.
%C The identity (5651522*n^2 - 2541672*n + 285769)^2 - (1681*n^2 - 756*n + 85)*(137842*n - 30996)^2 = 1 can be written as (A157106(n))^2 - (A157010(n))*(a(n))^2 = 1.
%H Vincenzo Librandi, <a href="/A157105/b157105.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = 2*a(n-1) -a(n-2).
%F G.f: 82*x*(1303 + 378*x)/(1-x)^2.
%F E.g.f.: 82*(378 - (378 - 1681*x)*exp(x)). - _G. C. Greubel_, Jan 11 2022
%t LinearRecurrence[{2,-1},{106846,244688},30] (* _Harvey P. Dale_, Mar 31 2013 *)
%t 82*(1681*Range[30] -378) (* _G. C. Greubel_, Jan 11 2022 *)
%o (Magma) I:=[106846, 244688, 382530]; [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) = 137842*n - 30996
%o (Sage) [82*(1681*n - 378) for n in (1..30)] # _G. C. Greubel_, Jan 11 2022
%Y Cf. A157010, A157106.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 23 2009
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