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A140359 a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3).

%I A140359 #23 Sep 08 2022 08:45:34
%S A140359 1,1,6,11,26,51,106,211,426,851,1706,3411,6826,13651,27306,54611,
%T A140359 109226,218451,436906,873811,1747626,3495251,6990506,13981011,
%U A140359 27962026,55924051,111848106,223696211,447392426,894784851,1789569706,3579139411
%N A140359 a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3).
%C A140359 This is the sequence A(1,1;1,2;3) of the family of sequences [a,b:c,d:k] considered by G. Detlefs, and treated as A(a,b;c,d;k) in the W. Lang link given below. - _Wolfdieter Lang_, Oct 18 2010
%H A140359 G. C. Greubel, <a href="/A140359/b140359.txt">Table of n, a(n) for n = 0..1000</a>
%H A140359 Wolfdieter Lang, <a href="/A140359/a140359.pdf">Notes on certain inhomogeneous three term recurrences.</a>
%H A140359 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2).
%F A140359 a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3).
%F A140359 a(n+1) - a(n) = 5*A001045(n), Jacobsthal numbers.
%F A140359 a(n+1) - 2*a(n) = (-1)^(n+1)* A010685(n).
%F A140359 From _R. J. Mathar_, Jul 10 2008: (Start)
%F A140359 O.g.f.: (1-x+3*x^2)/((x-1)*(2*x-1)*(1+x)).
%F A140359 a(n) = (5*2^(n+1) - 9 + 5*(-1)^n)/6. (End)
%F A140359 a(n) = a(n-1) + 2*a(n-2) +3, n>1 - _Gary Detlefs_, Jun 20 2010
%t A140359 Table[(5*2^(n+1) -9 + 5*(-1)^n)/6, {n, 0, 50}] (* _G. C. Greubel_, Oct 10 2017 *)
%t A140359 LinearRecurrence[{2,1,-2},{1,1,6},40] (* _Harvey P. Dale_, Mar 24 2021 *)
%o A140359 (PARI) for(n=0,50, print1((5*2^(n+1) -9 + 5*(-1)^n)/6, ", ")) \\ _G. C. Greubel_, Oct 10 2017
%o A140359 (Magma) [(5*2^(n+1) -9 + 5*(-1)^n)/6: n in [0..50]]; // _G. C. Greubel_, Oct 10 2017
%Y A140359 Cf. A000975, A001045, A087288, A137241, A140360.
%K A140359 nonn
%O A140359 0,3
%A A140359 _Paul Curtz_, Jun 24 2008
%E A140359 Extended by _R. J. Mathar_, Jul 10 2008