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A157105 137842n - 30996. 4

%I

%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 137842n - 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: x*(106846+30996*x)/(x-1)^2.

%t LinearRecurrence[{2,-1},{106846,244688},30] (* _Harvey P. Dale_, Mar 31 2013 *)

%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

%Y Cf. A157010, A157106.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Feb 23 2009

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Last modified June 12 19:06 EDT 2021. Contains 344959 sequences. (Running on oeis4.)