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 A145301 a(n) = 12*a(n-1) - 30*a(n-2) with a(0)=1 and a(1)=6. 7

%I

%S 1,6,42,324,2628,21816,182952,1540944,13002768,109804896,927575712,

%T 7836761664,66213868608,559463573376,4727146822272,39941854665984,

%U 337487851323648,2851598575904256,24094547371141632,203586611176571904,1720202912984613888

%N a(n) = 12*a(n-1) - 30*a(n-2) with a(0)=1 and a(1)=6.

%C Binomial transform is A152262, inverse binomial transform is A146962.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12, -30).

%F G.f.: (1-6x)/(1-12x+30x^2). - _R. J. Mathar_, Oct 10 2008

%F a(n) = ((6+sqrt(6))^n+(6-sqrt(6))^n)/2.

%F a(n) = sum_{k, 0<=k<=n} 6^k * A098158(n,k). - _Philippe Deléham_, Oct 14 2008

%t CoefficientList[Series[(1 - 6 x)/(1 - 12 x + 30 x^2), {x, 0, 20}], x] (* _Wesley Ivan Hurt_, Jun 14 2014 *)

%o (MAGMA) Z<x>:= PolynomialRing(Integers()); N<r6>:=NumberField(x^2-6); S:=[ ((6+r6)^n+(6-r6)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Oct 20 2008

%Y Cf. A098158, A152262, A146962.

%K nonn

%O 0,2

%A Al Hakanson (hawkuu(AT)gmail.com), Oct 06 2008

%E More terms from _R. J. Mathar_, Oct 10 2008

%E Corrected definition. - _Philippe Deléham_, Oct 15 2008

%E Edited by _Klaus Brockhaus_, Jul 08 2009

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Last modified April 24 04:23 EDT 2019. Contains 322406 sequences. (Running on oeis4.)