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A144720 a(0) = 2, a(1) = 3, a(n) = 4 * a(n-1) - a(n-2). 1

%I #9 Jan 03 2024 23:43:22

%S 2,3,10,37,138,515,1922,7173,26770,99907,372858,1391525,5193242,

%T 19381443,72332530,269948677,1007462178,3759900035,14032137962,

%U 52368651813,195442469290,729401225347,2722162432098,10159248503045

%N a(0) = 2, a(1) = 3, a(n) = 4 * a(n-1) - a(n-2).

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-1).

%F Sequence satisfies -11 = f(a(n), a(n+1)) where f(u, v) = u^2 + v^2 - 4*u*v.

%F G.f.: (2 - 5*x) / (1 - 4*x + x^2). a(n) = (11 + a(n-1)^2) / a(n-2).

%t LinearRecurrence[{4,-1},{2,3},30] (* _Harvey P. Dale_, Aug 29 2015 *)

%o (PARI) {a(n) = real( (2 + quadgen(12))^n * ( 2 - 1 / quadgen(12) ))}

%o (PARI) {a(n) = subst( (4*polchebyshev(n) + polchebyshev(n-1)) / 3, x, 2)}

%Y Cf. A144721(n) = a(-n).

%K nonn

%O 0,1

%A _Michael Somos_, Sep 19 2008

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Last modified June 17 18:04 EDT 2024. Contains 373463 sequences. (Running on oeis4.)