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Expansion of 1+x*(2+3*x)/(1-4*x^2).
5

%I #19 Aug 18 2022 08:29:31

%S 1,2,3,8,12,32,48,128,192,512,768,2048,3072,8192,12288,32768,49152,

%T 131072,196608,524288,786432,2097152,3145728,8388608,12582912,

%U 33554432,50331648,134217728,201326592,536870912,805306368,2147483648,3221225472

%N Expansion of 1+x*(2+3*x)/(1-4*x^2).

%C A002001 interleaved with A081294. _Gary W. Adamson_, Jul 08 2012

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,4).

%F a(n) = 2*a(n-1)-(-1)^n*A131577(n-1), n>0.

%F a(n) = 4*a(n-2), n>2. _Gary W. Adamson_, Jul 08 2012

%F a(n) = 2^(n-3)*(7-(-1)^n), n>0. - _R. J. Mathar_, Jul 22 2012

%F Sum_{n>=0} 1/a(n) = 19/9. - _Amiram Eldar_, Aug 18 2022

%p A134683 := proc(n)

%p if n =0 then

%p 1 ;

%p else

%p -(-1)^n*A131577(n-1)+2*procname(n-1) ;

%p end if;

%p end proc: # _R. J. Mathar_, Jul 22 2012

%t CoefficientList[Series[1 + x*(2 + 3*x)/(1 - 4*x^2), {x, 0, 32}], x] (* _Amiram Eldar_, Aug 18 2022 *)

%Y Cf. A001045, A045623, A131577, A002001, A081294, A000302.

%K nonn,easy

%O 0,2

%A _Paul Curtz_, Jan 26 2008, Feb 09 2008

%E Edited by _N. J. A. Sloane_, Feb 20 2008