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 A084069 Numbers n such that 7*n^2 = floor(n*sqrt(7)*ceil(n*sqrt(7))). 3

%I

%S 1,3,17,48,271,765,4319,12192,68833,194307,1097009,3096720,17483311,

%T 49353213,278635967,786554688,4440692161,12535521795,70772438609,

%U 199781794032,1127918325583,3183973182717,17975920770719,50743789129440

%N Numbers n such that 7*n^2 = floor(n*sqrt(7)*ceil(n*sqrt(7))).

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,16,0,-1).

%F a(1)=1, a(2)=3, a(2n)=6*a(2n-1)-a(2n-2); a(2n+1)=3*a(2n)-a(2n-1)

%F a(n)a(n+3) = -3 + a(n+1)a(n+2).

%F G.f.: x*(1+3*x+x^2)/(1-16*x^2+x^4).

%F a(n)=16*a(n-2)-a(n-4), n>4. [From Harvey P. Dale, Oct 31 2011]

%t CoefficientList[Series[(1+3x+x^2)/(1-16x^2+x^4),{x,0,30}],x] (* or *) LinearRecurrence[{0,16,0,-1},{1,3,17,48},31] (* _Harvey P. Dale_, Oct 31 2011 *)

%Y Cf. A159678, A001080, A001653, A001353, A060645, A001078, A001109, A084068, A084070.

%K nonn

%O 1,2

%A _Benoit Cloitre_, May 10 2003

%E Corrected formula for generating function [Harvey P. Dale, Oct 31 2011]

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Last modified June 24 09:37 EDT 2019. Contains 324323 sequences. (Running on oeis4.)