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A137208 a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) for n > 2; a(0)=2, a(1)=3, a(2)=6.

%I A137208 #24 Jan 02 2024 08:58:09
%S A137208 2,3,6,10,22,38,86,150,342,598,1366,2390,5462,9558,21846,38230,87382,
%T A137208 152918,349526,611670,1398102,2446678,5592406,9786710,22369622,
%U A137208 39146838,89478486,156587350,357913942,626349398,1431655766,2505397590,5726623062,10021590358
%N A137208 a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) for n > 2; a(0)=2, a(1)=3, a(2)=6.
%H A137208 Vincenzo Librandi, <a href="/A137208/b137208.txt">Table of n, a(n) for n = 0..1000</a>
%H A137208 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 4, -4).
%F A137208 G.f.: (2 + x - 5*x^2) / ((1 - x)*(1 - 2*x)*(1 + 2*x)). - _Colin Barker_, Jan 22 2017
%p A137208 a:=proc(n) option remember; if n=0 then 2 elif n=1 then 3 elif n=2 then 6 else a(n-1)+4*a(n-2)-4*a(n-3); fi; end: seq(a(n), n=0..50); # _Wesley Ivan Hurt_, Jan 21 2017
%t A137208 LinearRecurrence[{1,4,-4},{2,3,6},40] (* _Harvey P. Dale_, Sep 04 2018 *)
%o A137208 (Magma)[(2/3)+(5/4)*2^n+(1/12)*(-2)^n: n in [0..40]]; // _Vincenzo Librandi_, Aug 09 2011
%o A137208 (PARI) Vec((2 + x - 5*x^2) / ((1 - x)*(1 - 2*x)*(1 + 2*x)) + O(x^40)) \\ _Colin Barker_, Jan 22 2017
%Y A137208 Cf. A097164.
%K A137208 nonn,easy
%O A137208 0,1
%A A137208 _Paul Curtz_, Mar 05 2008
%E A137208 Extended by _Vincenzo Librandi_, Aug 09 2011