A087211 a(n) = floor((1+2^n+3^n)/3).
1, 2, 4, 12, 32, 92, 264, 772, 2272, 6732, 20024, 59732, 178512, 534172, 1599784, 4793892, 14370752, 43090412, 129227544, 387595252, 1162610992, 3487483452, 10461751304, 31383855812, 94148771232, 282440721292, 847310979064
Offset: 0
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-1,-6).
Programs
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Mathematica
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 *)
Formula
G.f.: (1-2*x-3*x^2+4*x^3)/((1+x)*(1-2*x)*(1-3*x));
E.g.f.: (exp(3*x)+exp(2*x)+2*exp(0)-exp(-x))/3;
a(n) = (3^n+2^n+2*0^n-(-1)^n)/3.
a(n) = 2*A094039(n), n>0. - R. J. Mathar, Feb 13 2015
a(n) = 4*a(n-1) - a(n-2) - 6*a(n-3). - Wesley Ivan Hurt, Apr 25 2023