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%I #28 Sep 08 2022 08:45:32
%S 0,1,1,2,6,8,20,40,72,160,304,608,1248,2432,4928,9856,19584,39424,
%T 78592,157184,314880,628736,1258496,2516992,5031936,10067968,20131840,
%U 40263680,80535552,161054720,322125824,644251648,1288470528,2577006592,5153947648,10307895296
%N a(n) = 2*a(n-2) + 4*a(n-3), with initial terms 0, 1, 1.
%H Robert Israel, <a href="/A134136/b134136.txt">Table of n, a(n) for n = 0..2991</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,4).
%F a(n) = (6*2^n - (3+i)*(-1+i)^n - (3-i)*(-1-i)^n)/20. - _Ivan Neretin_, May 27 2015
%F G.f.: (x^2+x)/(1-2*x^2-4*x^3). - _Robert Israel_, May 27 2015
%p f:= gfun:-rectoproc({a(n)=2*a(n-2)+4*a(n-3), a(0)=0,a(1)=1,a(2)=1},a(n),remember):
%p seq(f(n),n=0..100); # _Robert Israel_, May 27 2015
%t Nest[Append[#, 2 #[[-2]] + 4 #[[-3]]] &, {0, 1, 1}, 15] (* _Ivan Neretin_, May 27 2015 *)
%t CoefficientList[Series[x (1 + x)/((1 - 2 x) (2 x^2 + 2 x + 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, May 28 2015 *)
%o (Magma) [n le 3 select Floor(n/2) else 2*Self(n-2)+4*Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, May 28 2015
%Y Cf. A134654.
%K nonn,easy
%O 0,4
%A _Paul Curtz_, Jan 29 2008
%E More terms from _Robert Israel_, May 27 2015
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