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%I #7 Oct 30 2017 05:19:35
%S 0,1,3,6,12,27,63,141,297,594,1146,2169,4095,7827,15291,30582,62256,
%T 127791,262143,534129,1078101,2156202,4282878,8477181,16777215,
%U 33288711,66311703,132623406,266043972,534479427,1073741823,2154658101
%N Binomial transform of A088689.
%F a(n) = 2^n - cos(Pi*n/3) - 3^(n/2)*sin(Pi*n/6)/sqrt(3).
%F O.g.f.: -x(1-3x+3x^2+x^3)/[(2x-1)(x^2-x+1)(3x^2-3x+1)]. - _R. J. Mathar_, Apr 02 2008
%t Table[Sum[Binomial[n,k] * Mod[k*Floor[3*(k+1)/2] - 2*k, 3], {k, 0, n}], {n, 0, 40}] (* _Vaclav Kotesovec_, Oct 30 2017 *)
%Y Cf. A001045.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Oct 06 2003
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