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%I #13 Apr 25 2023 13:26:14
%S 1,2,4,12,32,92,264,772,2272,6732,20024,59732,178512,534172,1599784,
%T 4793892,14370752,43090412,129227544,387595252,1162610992,3487483452,
%U 10461751304,31383855812,94148771232,282440721292,847310979064
%N a(n) = floor((1+2^n+3^n)/3).
%H Harvey P. Dale, <a href="/A087211/b087211.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-1,-6).
%F G.f.: (1-2*x-3*x^2+4*x^3)/((1+x)*(1-2*x)*(1-3*x));
%F E.g.f.: (exp(3*x)+exp(2*x)+2*exp(0)-exp(-x))/3;
%F a(n) = (3^n+2^n+2*0^n-(-1)^n)/3.
%F a(n) = 2*A094039(n), n>0. - _R. J. Mathar_, Feb 13 2015
%F a(n) = 4*a(n-1) - a(n-2) - 6*a(n-3). - _Wesley Ivan Hurt_, Apr 25 2023
%t Table[Floor[(1+2^n+3^n)/3],{n,0,30}] (* or *) LinearRecurrence[{4,-1,-6},{1,2,4,12},30] (* _Harvey P. Dale_, May 21 2018 *)
%Y Cf. A011782, A094039.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Aug 26 2003
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