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%I #18 Mar 26 2024 10:30:18
%S 1,6,5,22,13,74,29,262,69,986,197,3846,669,15242,2509,60774,9813,
%T 242842,38965,971046,155501,3883786,621565,15534662,2485733,62138074,
%U 9942309,248551622,39768509,994205706,159073197,3976821926,636291829
%N a(0)=1, a(n)=2^n+n^2-2*a(n-1).
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-11,12,-4).
%F a(2n)=(1/27)*(25*4^n+36*n^2+24*n+2); a(2n+1)=(1/27)*(4*4^n+36*n^2+60*n+23)
%F a(0)=1, a(1)=1, a(2)=6, a(3)=5, a(4)=22, a(n)=3*a(n-1)+a(n-2)- 11*a(n-3)+ 12*a(n-4)-4*a(n-5) [From Harvey P. Dale, Apr 25 2012]
%F G.f.: -(4*x^4-12*x^3+14*x^2-3*x-1) / ((x-1)^3*(2*x-1)*(2*x+1)). [_Colin Barker_, Jun 26 2013]
%t RecurrenceTable[{a[0]==1,a[n]==2^n+n^2-2a[n-1]},a,{n,40}] (* or *) LinearRecurrence[{3,1,-11,12,-4},{1,1,6,5,22},40] (* _Harvey P. Dale_, Apr 25 2012 *)
%o (PARI) a(n)=if(n<1,1,2^n+n^2-2*a(n-1))
%K nonn,easy
%O 0,2
%A _Benoit Cloitre_, Apr 13 2003
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