Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #24 Jan 02 2024 08:58:09
%S 2,3,6,10,22,38,86,150,342,598,1366,2390,5462,9558,21846,38230,87382,
%T 152918,349526,611670,1398102,2446678,5592406,9786710,22369622,
%U 39146838,89478486,156587350,357913942,626349398,1431655766,2505397590,5726623062,10021590358
%N 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 Vincenzo Librandi, <a href="/A137208/b137208.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 (1, 4, -4).
%F G.f.: (2 + x - 5*x^2) / ((1 - x)*(1 - 2*x)*(1 + 2*x)). - _Colin Barker_, Jan 22 2017
%p 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 LinearRecurrence[{1,4,-4},{2,3,6},40] (* _Harvey P. Dale_, Sep 04 2018 *)
%o (Magma)[(2/3)+(5/4)*2^n+(1/12)*(-2)^n: n in [0..40]]; // _Vincenzo Librandi_, Aug 09 2011
%o (PARI) Vec((2 + x - 5*x^2) / ((1 - x)*(1 - 2*x)*(1 + 2*x)) + O(x^40)) \\ _Colin Barker_, Jan 22 2017
%Y Cf. A097164.
%K nonn,easy
%O 0,1
%A _Paul Curtz_, Mar 05 2008
%E Extended by _Vincenzo Librandi_, Aug 09 2011