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a(1)=1; a(n) = floor((3 + sqrt(21))*a(n-1)/2) for n > 1.
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%I #27 Apr 10 2024 03:45:12

%S 1,3,11,41,155,587,2225,8435,31979,121241,459659,1742699,6607073,

%T 25049315,94969163,360055433,1365073787,5175387659,19621384337,

%U 74390315987,282035100971,1069276250873

%N a(1)=1; a(n) = floor((3 + sqrt(21))*a(n-1)/2) for n > 1.

%C Contains only odd numbers.

%H Vincenzo Librandi, <a href="/A196472/b196472.txt">Table of n, a(n) for n = 1..150</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,-3)

%F G.f.: -x*(-1+ x + x ^2) / ( (x-1)*(3*x^2 + 3*x - 1) ). - _R. J. Mathar_, Oct 04 2011

%F a(n) = (3 + 2*A108306(n))/15. - _R. J. Mathar_, Oct 04 2011

%t With[{c=(3+Sqrt[21])/2},NestList[Floor[c*#]&,1,30]] (* _Harvey P. Dale_, Apr 23 2014 *)

%o (Magma) I:=[1,3,11]; [n le 3 select I[n] else 4*Self(n-1)-3*Self(n-3): n in [1..30]]: // _Vincenzo Librandi_, Oct 05 2011

%Y Cf. A108306.

%K nonn,easy

%O 1,2

%A _Philippe Deléham_, Oct 03 2011