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%I #16 Sep 08 2022 08:45:32
%S 0,0,3,1,11,6,42,21,171,85,683,342,2730,1365,10923,5461,43691,21846,
%T 174762,87381,699051,349525,2796203,1398102,11184810,5592405,44739243,
%U 22369621,178956971,89478486,715827882,357913941,2863311531,1431655765
%N A024495 but with terms swapped in pairs.
%H G. C. Greubel, <a href="/A135574/b135574.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,3,0,4).
%F a(n+1) - 2*a(n) = A135575(n).
%F O.g.f.: x^2*(3 + x +2*x^2 +3*x^3)/((1-2*x)*(1+2*x)*(x^2-x+1)*(x^2+x+1)). - _R. J. Mathar_, Mar 31 2008
%F a(n) = 3*a(n-2) + 3*a(n-4) + 4*a(n-6). - _G. C. Greubel_, Oct 19 2016
%F a(n) = (1/6)*(2^(n-1)*(5+3*(-1)^n) - (1+3*(-1)^n)*ChebyshevU(n, 1/2) - (1-3*(-1)^n)*ChebyshevU(n-1, 1/2)). - _G. C. Greubel_, Jan 05 2022
%p A024495 := proc(n) option remember ; if n <=1 then 0; elif n = 2 then 1; else 3*procname(n-1)-3*procname(n-2)+2*procname(n-3) ; fi; end: A135574 := proc(n) option remember ; if n mod 2 = 0 then A024495(n+1) ; else A024495(n-1) ; fi; end: seq(A135574(n),n=0..40) ; # _R. J. Mathar_, Feb 07 2009
%t LinearRecurrence[{0,3,0,3,0,4},{0,0,3,1,11,6},41] (* _G. C. Greubel_, Oct 19 2016 *)
%o (Magma) I:=[0,0,3,1,11,6]; [n le 6 select I[n] else 3*Self(n-2) +3*Self(n-4) +4*Self(n-6): n in [1..41]]; // _G. C. Greubel_, Jan 05 2022
%o (Sage) [(1/6)*(2^(n-1)*(5+3*(-1)^n) - (1+3*(-1)^n)*chebyshev_U(n, 1/2) - (1-3*(-1)^n)*chebyshev_U(n-1, 1/2)) for n in (0..40)] # _G. C. Greubel_, Jan 05 2022
%Y Cf. A010892, A024495, A135575.
%K nonn,easy
%O 0,3
%A _Paul Curtz_, Feb 24 2008
%E More terms from _R. J. Mathar_, Mar 31 2008
%E More terms from _R. J. Mathar_, Feb 07 2009
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