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A105082 Expansion of (5+4x)/(1-2x-x^2).

%I A105082 #24 Jan 05 2025 19:51:38
%S A105082 5,14,33,80,193,466,1125,2716,6557,15830,38217,92264,222745,537754,
%T A105082 1298253,3134260,7566773,18267806,44102385,106472576,257047537,
%U A105082 620567650,1498182837,3616933324,8732049485,21081032294,50894114073
%N A105082 Expansion of (5+4x)/(1-2x-x^2).
%C A105082 A floretion-generated, Pellian related sequence.
%C A105082 Floretion Algebra Multiplication Program, FAMP Code: lesloop(infty)-tesforseq[ + .25'i + .25i' - .25'ii' - .25'jj' - .25'kk' + .25'jk' + .25'kj' - .25e ], Fortype: 1A.
%C A105082 For n > 0: A048696(n) = a(n) - a(n-1). - _Reinhard Zumkeller_, Dec 15 2013
%H A105082 Reinhard Zumkeller, <a href="/A105082/b105082.txt">Table of n, a(n) for n = 0..1000</a>
%H A105082 A. F. Horadam, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/9-3/horadam-a.pdf">Pell Identities</a>, Fib. Quart., Vol. 9, No. 3, 1971, pp. 245-252.
%H A105082 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A105082 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,1).
%F A105082 a(n+2) = 2*a(n+1) + a(n); FAMP result: a(n) = 2*A001333(n) + 3*A048654(n); SuperSeeker results: a(n+1) - a(n) = A048696(n+1); a(n) + a(n+1) = A048696(n+2)
%F A105082 a(n) = ((9+5*sqrt(2))*(1+sqrt(2))^n - (9-5*sqrt(2))*(1-sqrt(2))^n)/(2*sqrt(2)) - Lambert Herrgesell (zero815(AT)googlemail.com), Jan 26 2007
%o A105082 (Haskell)
%o A105082 a105082 n = a105082_list !! n
%o A105082 a105082_list = scanl (+) 5 $ tail a048696_list
%o A105082 -- _Reinhard Zumkeller_, Dec 15 2013
%Y A105082 Cf. A001333, A048654, A048696.
%Y A105082 Cf. A048772.
%K A105082 nonn,easy
%O A105082 0,1
%A A105082 _Creighton Dement_, Apr 06 2005