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%I #20 Mar 26 2024 10:30:42
%S 1,1,4,3,14,9,52,31,202,117,800,459,3190,1825,12748,7287,50978,29133,
%T 203896,116515,815566,466041,3262244,1864143,13048954,7456549,
%U 52195792,29826171,208783142,119304657,835132540,477218599,3340530130,1908874365
%N a(0)=1, a(n)=2^n+n-2*a(n-1).
%H Harvey P. Dale, <a href="/A082383/b082383.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,-8,4).
%F a(2n) = (1/9)*(7*4^n+6*n+2); a(2n+1) = (1/9)*(4*4^n+6*n+5).
%F a(n) = 2*a(n-1)+3*a(n-2)-8*a(n-3)+4*a(n-4). G.f.: (x^2+x-1) / ((x-1)^2*(2*x-1)*(2*x+1)). - _Colin Barker_, Jun 26 2013
%t RecurrenceTable[{a[0]==1,a[n]==2^n+n-2a[n-1]},a,{n,40}] (* or *) LinearRecurrence[{2,3,-8,4},{1,1,4,3},40] (* _Harvey P. Dale_, Mar 09 2014 *)
%o (PARI) a(n)=if(n<1,1,2^n+n-2*a(n-1))
%K nonn,easy
%O 0,3
%A _Benoit Cloitre_, Apr 13 2003
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