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A127985 a(n) = floor(2^n*(n/3 + 4/9)).

%I A127985 #38 May 25 2023 16:13:42
%S A127985 0,1,4,11,28,67,156,355,796,1763,3868,8419,18204,39139,83740,178403,
%T A127985 378652,800995,1689372,3553507,7456540,15612131,32622364,68040931,
%U A127985 141674268,294533347,611436316,1267611875,2624702236,5428361443
%N A127985 a(n) = floor(2^n*(n/3 + 4/9)).
%H A127985 Vincenzo Librandi, <a href="/A127985/b127985.txt">Table of n, a(n) for n = 0..1000</a> (corrected by Ray Chandler, Jan 19 2019)
%H A127985 Wieb Bosma, <a href="http://dx.doi.org/10.5802/jtnb.301">Signed bits and fast exponentiation</a>, J. Th. Nombres de Bordeaux, 13 no. 1 (2001), p. 27-41.
%H A127985 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,-4,4).
%F A127985 a(n) = (n/3 + 4/9)*2^n - 1/2 + (-1)^n/18.
%F A127985 a(1)=1, a(2)=4, a(3)=11, a(4)=28, a(n) = 4*a(n-1)-3*a(n-2)-4*a(n-3)+4*a(n-4). - _Harvey P. Dale_, May 15 2011
%F A127985 G.f.: x*(1-2*x^2)/((1-2*x)^2*(1-x^2)). - _Harvey P. Dale_, May 15 2011
%F A127985 E.g.f.: ((4 + 6*x)*cosh(2*x) - 5*sinh(x) + 4*cosh(x)*((2 + 3*x)*sinh(x) - 1))/9. - _Stefano Spezia_, May 25 2023
%t A127985 Table[(n/3 + 4/9) 2^n - 1/2 + (-1)^n/18, {n, 1, 50}]
%t A127985 LinearRecurrence[{4,-3,-4,4},{1,4,11,28},50] (* _Harvey P. Dale_, May 15 2011 *)
%o A127985 (Magma) [(n/3 + 4/9)*2^n - 1/2 + (-1)^n/18: n in [1..40]]; // _Vincenzo Librandi_, May 26 2011
%o A127985 (PARI) a(n)=(n*3+4)<<n\9 \\ _M. F. Hasler_, Oct 07 2014
%Y A127985 Cf. A073371, A127976, A127978, A127979, A127980, A127981, A127982, A127983, A127984, A073371, A000337.
%K A127985 nonn,easy
%O A127985 0,3
%A A127985 _Artur Jasinski_, Feb 09 2007
%E A127985 Definition simplified by _M. F. Hasler_, Oct 07 2014
%E A127985 Sequence extended to a(0)=0 by _M. F. Hasler_, Oct 08 2014