Search: id:A048654
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%I A048654
%S A048654 1,4,9,22,53,128,309,746,1801,4348,10497,25342,61181,147704,356589,
%T A048654 860882,2078353,5017588,12113529,29244646,70602821,170450288,411503397,
%U A048654 993457082,2398417561,5790292204
%N A048654 a(n)=2a(n-1)+a(n-2); a(0)=1, a(1)=4.
%C A048654 Generalized Pellian with second term equal to 4.
%C A048654 The generalized Pellian with second term equal to s has the terms a(n) 
               = A000129(n)*s+A00129(n-1). The generating function is -(1+s*x-2*x)/
               (-1+2*x+x^2) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 
               22 2007
%D A048654 A. F. Horadam, Pell Identities, Fibonacci Quarterly, Vol. 9, No. 3, 1971, 
               pp. 245-252.
%D A048654 A. F. Horadam, Basic Properties of a Certain Generalized Sequence of 
               Numbers, Fibonacci Quarterly, Vol. 3, No. 3, 1965, pp. 161-176.
%D A048654 A. F. Horadam, Special Properties of the Sequence W(a, b; p, q), Fibonacci 
               Quarterly, Vol. 5, No. 5, 1967, pp. 424-434.
%H A048654 T. D. Noe, <a href="b048654.txt">Table of n, a(n) for n=0..300</a>
%H A048654 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A048654 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A048654 a(n)=[ (3+sqrt(2))(1+sqrt(2))^n - (3-sqrt(2))(1-sqrt(2))^n ]/2*sqrt(2).
%F A048654 A048654(n) = 2P(n+2) - 3P(n+1), P(n) = Pell numbers (A000129) - Creighton 
               Dement (creighton.k.dement(AT)uni-oldenburg.de), Oct 27 2004
%F A048654 G.f.: (1+2*x)/(1-2*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 03 2008]
%F A048654 a(n)=binomial transform of 1,3,2,6,4,12 [From Al Hakanson (hawkuu(AT)gmail.com), 
               Aug 08 2009]
%p A048654 with(combinat): a:=n->2*fibonacci(n-1,2)+fibonacci(n,2): seq(a(n), n=1..26); 
               - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 04 2008
%t A048654 a=2;b=1;c=1;lst={b};Do[c=a+b+c;AppendTo[lst,c];a=b;b=c,{n,5!}];lst [From 
               Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 23 2009]
%Y A048654 Cf. A001333, A000129, A048655, A038761, A100525.
%Y A048654 Sequence in context: A032288 A076859 A042833 this_sequence A122626 A135025 
               A070713
%Y A048654 Adjacent sequences: A048651 A048652 A048653 this_sequence A048655 A048656 
               A048657
%K A048654 easy,nice,nonn
%O A048654 0,2
%A A048654 Barry E. Williams

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