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A123270 a(0)=1, a(1)=1, a(n) = 5*a(n-1) + 4*a(n-2).

%I A123270 #29 Dec 31 2023 11:29:44
%S A123270 1,1,9,49,281,1601,9129,52049,296761,1692001,9647049,55003249,
%T A123270 313604441,1788035201,10194593769,58125109649,331403923321,
%U A123270 1889520055201,10773215969289,61424160067249,350213664213401,1996764961336001
%N A123270 a(0)=1, a(1)=1, a(n) = 5*a(n-1) + 4*a(n-2).
%C A123270 First differences give {0, 8, 40, 232, 1320, 7528, 42920, ...} = 8*A015537(n) = 8 * {0, 1, 5, 29, 165, 941, 5365, ...}. - _Alexander Adamchuk_, Nov 03 2006
%H A123270 Reinhard Zumkeller, <a href="/A123270/b123270.txt">Table of n, a(n) for n = 0..1000</a>
%H A123270 Lucyna Trojnar-Spelina, Iwona Włoch, <a href="https://doi.org/10.1007/s40995-019-00757-7">On Generalized Pell and Pell-Lucas Numbers</a>, Iranian Journal of Science and Technology, Transactions A: Science (2019), 1-7.
%H A123270 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5, 4).
%F A123270 a(n) = Sum_{k=0..n} 4^(n-k)*A122542(n,k).
%F A123270 G.f.: (1-4*x)/(1-5*x-4*x^2).
%F A123270 a(n) = 1 + 8*Sum_{k=0..n} A015537(k). - _Alexander Adamchuk_, Nov 03 2006
%t A123270 LinearRecurrence[{5,4},{1,1},30] (* _Harvey P. Dale_, Jul 25 2011 *)
%o A123270 (Haskell)
%o A123270 a123270 n = a123270_list !! n
%o A123270 a123270_list = 1 : 1 : zipWith (-) (map (* 5) $
%o A123270    zipWith (+) (tail a123270_list) a123270_list) a123270_list
%o A123270 -- _Reinhard Zumkeller_, Aug 16 2013
%Y A123270 Cf. A015537.
%Y A123270 Cf. A095344, A090390.
%K A123270 nonn
%O A123270 0,3
%A A123270 _Philippe Deléham_, Oct 09 2006