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A216714 a(n) = 2^(n-5) - A000931(n).

%I A216714 #28 Sep 08 2022 08:46:03
%S A216714 0,1,3,6,14,29,60,123,249,503,1012,2032,4075,8164,16347,32719,65471,
%T A216714 130986,262030,524137,1048376,2096887,4193953,8388143,16776600,
%U A216714 33553616,67107783,134216296,268433559,536868399,1073738495,2147479238,4294961454,8589926853,17179858932,34359724787,68719458745,137438929639,274877875372,549755772064
%N A216714 a(n) = 2^(n-5) - A000931(n).
%C A216714 It is conjectured that this sequence (with a different offset) and A038360 are the same.
%H A216714 Vincenzo Librandi, <a href="/A216714/b216714.txt">Table of n, a(n) for n = 5..1000</a>
%H A216714 P. Flajolet and B. Salvy, <a href="http://projecteuclid.org/euclid.em/1047674270">Euler sums and contour integral representations</a>, Experimental Mathematics, Vol. 7 Issue 1 (1998).
%H A216714 M. Waldschmidt, <a href="http://www.math.jussieu.fr/~miw/articles/pdf/MZV2011IMSc.pdf">Lectures on Multiple Zeta Values</a> (IMSC2011).
%H A216714 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-1,-2)
%F A216714 G.f.: -x^6*(-1-x+x^2) / ( (2*x-1)*(x^3+x^2-1) ). - _R. J. Mathar_, Sep 16 2012
%F A216714 a(n) = 2*a(n-1)+a(n-2)-a(n-3)-2*a(n-4). - _Vincenzo Librandi_, Mar 11 2013
%t A216714 CoefficientList[Series[-x (-1 - x + x^2)/((2 x - 1) (x^3 + x^2 - 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Mar 11 2013 *)
%t A216714 LinearRecurrence[{2,1,-1,-2},{0,1,3,6},40] (* _Harvey P. Dale_, Aug 22 2021 *)
%o A216714 (Magma) I:=[0, 1, 3, 6]; [n le 4 select I[n] else 2*Self(n-1)+Self(n-2)-Self(n-3)-2*Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Mar 11 2013
%o A216714 (PARI) a(n)=([0,1,0,0; 0,0,1,0; 0,0,0,1; -2,-1,1,2]^(n-5)*[0;1;3;6])[1,1] \\ _Charles R Greathouse IV_, Sep 09 2016
%Y A216714 Cf. A000931, A038360.
%K A216714 nonn,easy
%O A216714 5,3
%A A216714 _N. J. A. Sloane_, Sep 14 2012