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A134683 Expansion of 1+x*(2+3*x)/(1-4*x^2).

%I A134683 #19 Aug 18 2022 08:29:31
%S A134683 1,2,3,8,12,32,48,128,192,512,768,2048,3072,8192,12288,32768,49152,
%T A134683 131072,196608,524288,786432,2097152,3145728,8388608,12582912,
%U A134683 33554432,50331648,134217728,201326592,536870912,805306368,2147483648,3221225472
%N A134683 Expansion of 1+x*(2+3*x)/(1-4*x^2).
%C A134683 A002001 interleaved with A081294. _Gary W. Adamson_, Jul 08 2012
%H A134683 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,4).
%F A134683 a(n) = 2*a(n-1)-(-1)^n*A131577(n-1), n>0.
%F A134683 a(n) = 4*a(n-2), n>2. _Gary W. Adamson_, Jul 08 2012
%F A134683 a(n) = 2^(n-3)*(7-(-1)^n), n>0. - _R. J. Mathar_, Jul 22 2012
%F A134683 Sum_{n>=0} 1/a(n) = 19/9. - _Amiram Eldar_, Aug 18 2022
%p A134683 A134683 := proc(n)
%p A134683     if n =0 then
%p A134683         1 ;
%p A134683     else
%p A134683         -(-1)^n*A131577(n-1)+2*procname(n-1) ;
%p A134683     end if;
%p A134683 end proc: # _R. J. Mathar_, Jul 22 2012
%t A134683 CoefficientList[Series[1 + x*(2 + 3*x)/(1 - 4*x^2), {x, 0, 32}], x] (* _Amiram Eldar_, Aug 18 2022 *)
%Y A134683 Cf. A001045, A045623, A131577, A002001, A081294, A000302.
%K A134683 nonn,easy
%O A134683 0,2
%A A134683 _Paul Curtz_, Jan 26 2008, Feb 09 2008
%E A134683 Edited by _N. J. A. Sloane_, Feb 20 2008