cp's OEIS Frontend

A087161 Records in A087159, i.e., A087159(a(n)) = n, and satisfies the recurrence a(n+3) = 5*a(n+2) - 6* a(n+1) + 2*a(n) with a(1) = 1, a(2) = 2, and a(3) = 4.

%I A087161 #26 Feb 10 2021 08:25:03
%S A087161 1,2,4,10,30,98,330,1122,3826,13058,44578,152194,519618,1774082,
%T A087161 6057090,20680194,70606594,241065986,823050754,2810071042,9594182658,
%U A087161 32756588546,111837988866,381838778370,1303679135746,4451038986242
%N A087161 Records in A087159, i.e., A087159(a(n)) = n, and satisfies the recurrence a(n+3) = 5*a(n+2) - 6* a(n+1) + 2*a(n) with a(1) = 1, a(2) = 2, and a(3) = 4.
%C A087161 Binomial transform of A001333 (which, with an extra leading 1, is the expansion of (1 - x - 2*x^2)/(1 - 2*x - x^2)). - _Paul Barry_, Aug 26 2003
%C A087161 Partial sums of the binomial transform of Pell(n-1). - _Paul Barry_, Apr 24 2004
%H A087161 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-6,2).
%F A087161 G.f.: x*(1 - 3*x)/(1 - 5*x + 6*x^2 - 2*x^3).
%F A087161 a(n) = 2 + 2*A007070(n-3) for n > 2.
%F A087161 a(n) = ((2 - sqrt(2))^(n)/(1 - sqrt(2)) + (2 + sqrt(2))^(n)/(1 + sqrt(2)))/2 + 2 (offset 0) - _Paul Barry_, Aug 26 2003
%F A087161 a(n+1) - a(n) = A006012(n-1) for n >= 2. - _Philippe Deléham_, Feb 01 2012
%F A087161 a(1) = 1, a(2) = 2, a(3) = 4, a(n) = 5*a(n-1) - 6*a(n-2) + 2*a(n-3) for n >= 4. - _Harvey P. Dale_, Oct 12 2015
%F A087161 a(n+1) = Sum_{k=0..n} A100631(n,k) for n >= 0. - _Petros Hadjicostas_, Feb 09 2021
%t A087161 CoefficientList[Series[(1-3x)/(1-5x+6x^2-2x^3),{x,0,30}],x] (* or *) LinearRecurrence[{5,-6,2},{1,2,4},30] (* _Harvey P. Dale_, Oct 12 2015 *)
%Y A087161 Cf. A000129, A007070, A087159, A087160, A100631.
%K A087161 nonn
%O A087161 1,2
%A A087161 _Paul D. Hanna_, Aug 22 2003
%E A087161 More terms from _Paul Barry_, Apr 24 2004