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%I #11 Oct 11 2016 06:25:10
%S 1,4,13,51,204,819,3277,13108,52429,209715,838860,3355443,13421773,
%T 53687092,214748365,858993459,3435973836,13743895347,54975581389,
%U 219902325556,879609302221,3518437208883,14073748835532,56294995342131,225179981368525,900719925474100,3602879701896397,14411518807585587
%N a(n) = 3*a(n-1) + 4*a(n-2) - a(n-3) + 3*a(n-4) + 4*a(n-5).
%C Companion to A135343.
%H G. C. Greubel, <a href="/A135345/b135345.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,4,-1,3,4).
%F 4*a(n) - a(n+1) = hexaperiodic 0, 3, 1, 0, -3, -1.
%F a(n) = (4^(n+1)/5)-(2/15)*(-1)^n+(1/3)*cos(Pi*n/3)+(sqrt(3)/3)*cos(Pi*n/3). - _Richard Choulet_, Jan 04 2008
%F G.f.: ( -2*(3 + sqrt(3)) + (3 + 7*sqrt(3))*x + (9 + 5*sqrt(3))*x^2 -
%F 4*(3 + sqrt(3))*x^3)/( 6*(-1 + 4*x - x^3 + 4*x^4) ). - _G. C. Greubel_, Oct 10 2016
%F G.f.: (1-3*x^2) / ((1+x)*(1-4*x)*(1-x+x^2)). - _Colin Barker_, Oct 11 2016
%t LinearRecurrence[{3,4,-1,3,4},{1,4,13,51,204}, 25] (* _G. C. Greubel_, Oct 10 2016 *)
%o (PARI) Vec((1-3*x^2)/((1+x)*(1-4*x)*(1-x+x^2)) + O(x^30)) \\ _Colin Barker_, Oct 11 2016
%Y Cf. A135343.
%K nonn,easy
%O 0,2
%A _Paul Curtz_, Dec 06 2007
%E Removed incorrect formula, _Joerg Arndt_, Oct 11 2016
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