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A136249 a(n)=-a(n-1)+4*a(n-2)+4*a(n-3).

%I A136249 #25 Feb 27 2024 03:02:58
%S A136249 4,-2,1,7,-11,43,-59,187,-251,763,-1019,3067,-4091,12283,-16379,49147,
%T A136249 -65531,196603,-262139,786427,-1048571,3145723,-4194299,12582907,
%U A136249 -16777211,50331643,-67108859,201326587,-268435451,805306363,-1073741819,3221225467
%N A136249 a(n)=-a(n-1)+4*a(n-2)+4*a(n-3).
%H A136249 Vincenzo Librandi, <a href="/A136249/b136249.txt">Table of n, a(n) for n = 0..1000</a>
%H A136249 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1, 4, 4).
%F A136249 a(2*n)=5-2^(2*n), a(2*n+1)=10-3*a(2n).
%F A136249 a(n)+a(n+1)=A135520(n).
%F A136249 a(n) = 1/6*2^n*a(0) + 1/4*2^n*a(1) - 1/2*a(0)*(-2)^n - 1/3*(-1)^n*a(2) - 1/4*a(1)*(-2)^n + 4/3*(-1)^n*a(0) + 1/4*(-2)^n*a(2) + 1/12*2^n*a(2). - _Alexander R. Povolotsky_, Mar 31 2008
%F A136249 G.f.: (4+2*x-17*x^2)/((1+2*x)*(1-2*x)*(1+x)). a(n)=2^(n-2)+5*(-1)^n*(1-2^(n-2)). - _R. J. Mathar_, Jun 15 2009
%F A136249 a(n)=(5*(-2)^n-40*(-1)^n+2^n)/8. - _Harvey P. Dale_, Jun 10 2011
%t A136249 LinearRecurrence[{-1,4,4},{4,-2,1},50] (* or *) Table[(5(-2)^n- 40(-1)^n+2^n)/8,{n,50}] (* _Harvey P. Dale_, Jun 10 2011 *)
%o A136249 (Magma) [2^(n-2)+5*(-1)^n*(1-2^(n-2)): n in [0..40]]; // _Vincenzo Librandi_, Aug 09 2011
%Y A136249 Cf. A137241, A135529.
%K A136249 sign
%O A136249 0,1
%A A136249 _Paul Curtz_, Mar 17 2008
%E A136249 Edited by _N. J. A. Sloane_, Apr 18 2008
%E A136249 More terms from _Harvey P. Dale_, Jun 10 2011