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%I #7 Apr 13 2021 01:36:40
%S 1,2,4,9,19,41,87,185,391,825,1735,3641,7623,15929,33223,69177,143815,
%T 298553,618951,1281593,2650567,5475897,11301319,23301689,48001479,
%U 98799161,203190727,417566265,857502151,1759743545,3608965575
%N a(n) = 3*a(n-1) - 4*a(n-3), with a(0)=1, a(1)=2, a(2)=4, a(3)=9.
%H G. C. Greubel, <a href="/A136298/b136298.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 (3,0,-4).
%F From _R. J. Mathar_, Apr 04 2008: (Start)
%F O.g.f.: (1 -x -2*x^2 +x^3)/((1+x)*(1-2*x)^2).
%F a(n) = (7*2^n - (-1)^n)/9 + A001787(n+1)/12 if n>0. (End)
%F From _G. C. Greubel_, Apr 12 2021: (Start)
%F a(n) = (2^(n-2)*(3*n+31) - (-1)^n)/9 + (1/4)*[n=0].
%F E.g.f.: (1/36)*(9 - 4*exp(-x) + (31 + 6*x)*exp(2*x)). (End)
%t LinearRecurrence[{3,0,-4}, {1,2,4,9}, 41] (* _G. C. Greubel_, Apr 12 2021 *)
%o (Magma) [1] cat [(2^(n-2)*(31+3*n) - (-1)^n)/9: n in [1..40]]; // _G. C. Greubel_, Apr 12 2021
%o (Sage) [1]+[(2^(n-2)*(31+3*n) - (-1)^n)/9 for n in (1..40)] # _G. C. Greubel_, Apr 12 2021
%Y Cf. A001787, A078039.
%K nonn,easy
%O 0,2
%A _Paul Curtz_, Mar 22 2008
%E More terms from _R. J. Mathar_, Apr 04 2008
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