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%I #14 Sep 08 2022 08:45:23
%S 3,7,9,55,201,823,3273,13111,52425,209719,838857,3355447,13421769,
%T 53687095,214748361,858993463,3435973833,13743895351,54975581385,
%U 219902325559,879609302217,3518437208887,14073748835529,56294995342135
%N a(n) = 3*a(n-1) + 4*a(n-2), with a(0) = 3, a(1) = 7, a(3) = 9, for n > 2.
%H G. C. Greubel, <a href="/A115164/b115164.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,4).
%F From _Colin Barker_, Oct 31 2012: (Start)
%F a(n) = (4^(1 + n) - 19*(-1)^n)/5 for n > 0.
%F a(n) = 3*a(n-1) + 4*a(n-2) for n > 2.
%F G.f.: (24*x^2 + 2*x - 3)/((x + 1)*(4*x - 1)). (End)
%F From _Franck Maminirina Ramaharo_, Nov 23 2018: (Start)
%F a(n) = A115113(n) + A165326(n).
%F E.g.f.: (30 - 19*exp(-x) + 4*exp(4*x))/5. (End)
%t Join[{3}, LinearRecurrence[{3, 4}, {7, 9}, 50]]
%o (Maxima) (a[0] : 3, a[1] : 7, a[2] : 9, a[n] := 3*a[n-1] + 4*a[n-2], makelist(a[n], n, 0, 50)); /* _Franck Maminirina Ramaharo_, Nov 23 2018 */
%o (PARI) vector(50, n, n--; if(n==0, 3, (4^(1+n) -19*(-1)^n)/5)) \\ _G. C. Greubel_, Nov 23 2018
%o (Magma) [3] cat [(4^(1+n) -19*(-1)^n)/5: n in [1..50]]; // _G. C. Greubel_, Nov 23 2018
%o (Sage) [3] + [(4^(1+n) -19*(-1)^n)/5 for n in (1..50)] # _G. C. Greubel_, Nov 23 2018
%Y Cf. A115113, A115335.
%K nonn,easy
%O 0,1
%A _Roger L. Bagula_, Mar 06 2006
%E Edited, and new name from _Franck Maminirina Ramaharo_, Nov 23 2018, after _Colin Barker_
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