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a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 3, a(1) = 20.
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%I #15 Sep 08 2022 08:45:47

%S 3,20,118,664,3660,19984,108632,589280,3193392,17297216,93670240,

%T 507200896,2746223808,14868977920,80504690048,435871829504,

%U 2359908975360,12777066189824,69177803863552,374543504250880

%N a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 3, a(1) = 20.

%C Binomial transform of A164305. Fourth binomial transform of A164654. Inverse binomial transform of A164536.

%H Vincenzo Librandi, <a href="/A164535/b164535.txt">Table of n, a(n) for n = 0..158</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8, -14).

%F a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 3, a(1) = 20.

%F G.f.: (3-4*x)/(1-8*x+14*x^2).

%F a(n) = ((3+4*sqrt(2))*(4+sqrt(2))^n + (3-4*sqrt(2))*(4-sqrt(2))^n)/2.

%t CoefficientList[Series[(3-4x)/(1-8x+14x^2),{x,0,25}],x] (* _Harvey P. Dale_, Feb 23 2011 *)

%o (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+4*r)*(4+r)^n+(3-4*r)*(4-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Aug 20 2009

%Y Cf. A164305, A164654, A164536.

%K nonn,easy

%O 0,1

%A Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009

%E Edited and extended beyond a(5) by _Klaus Brockhaus_, Aug 20 2009