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%I #18 Sep 08 2022 08:45:35
%S 1,1,1,5,13,33,73,157,325,665,1345,2709,5437,10897,21817,43661,87349,
%T 174729,349489,699013,1398061,2796161,5592361,11184765,22369573,
%U 44739193,89478433,178956917,357913885,715827825,1431655705,2863311469,5726622997,11453246057,22906492177
%N a(n) = (2^(2+n)-(-1)^n)/3 - 2*n.
%H Vincenzo Librandi, <a href="/A141025/b141025.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 (3,-1,-3,2).
%F a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + 2*a(n-4).
%F a(n) = A001045(n+2) - 2*n.
%F a(n+1) - a(n) = 4*A000975(n-1).
%F a(n+1) - 2*a(n)= 2*(n-1) + (-1)^n = -1, -1, 3, 3, 7, 7, 11, 11,... duplicated A004767.
%F G.f. ( -1+2*x+x^2-6*x^3 ) / ( (1+x)*(2*x-1)*(x-1)^2 ). - _R. J. Mathar_, Jul 07 2011
%t CoefficientList[Series[(-1 + 2*x + x^2 - 6*x^3)/((1 + x)*(2*x - 1)*(x - 1)^2), {x, 0, 50}], x] (* _G. C. Greubel_, Oct 11 2017 *)
%o (Magma) [(2^(2+n)-(-1)^n)/3-2*n: n in [0..40]]; // _Vincenzo Librandi_, Aug 08 2011
%o (PARI) for(n=0,50, print1((2^(2+n)-(-1)^n)/3 - 2*n, ", ")) \\ _G. C. Greubel_, Oct 11 2017
%K nonn,easy
%O 0,4
%A _Paul Curtz_, Jul 29 2008
%E Definition replaced by closed form by _R. J. Mathar_, Jul 07 2011