Search: id:A038761
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%I A038761
%S A038761 1,9,53,309,1801,10497,61181,356589,2078353,12113529,70602821,
%T A038761 411503397,2398417561,13979001969,81475594253,474874563549,
%U A038761 2767771787041,16131756158697,94022765165141,548004834832149
%N A038761 a(n)=6a(n-1)-a(n-2), n >= 2, a(0)=1, a(1)=9.
%C A038761 Bisection of A048654. - Lambert Klasen (lambert.klasen(AT)gmx.de), Nov 
               24 2004
%C A038761 A Pellian-related sequence.
%C A038761 a(n)={9*([3+2*sqrt(2)]^n -[3-2*sqrt(2)]^n)-([3+2*sqrt(2)]^(n-1) - [3-2*sqrt(2)]^(n-1))}/
               (4*sqrt(2)).
%D A038761 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, 
               pp. 122-125, 194-196.
%D A038761 M. J. DeLeon, Pell's Equation and Pell Number Triples, Fib. Quart., 14(1976), 
               pp. 456-460.
%H A038761 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A038761 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A038761 A038761 = sqrt{2*(A038762)^2-14}/2.
%F A038761 For n>1, a(n)-4a(n-1)=A001541(n)-A001542(n-2); e.g. 309-4*53=97=99-2 
               - Charlie Marion (charliem(AT)bestweb.net), Nov 12 2003
%F A038761 For n>0, a(n)=A046090(n)+A001653(n)+A001652(n-1)=A055997(n+1)+A001652(n-1); 
               e.g., 309=120+169+20 - Charlie Marion (charliemath(AT)optonline.net), 
               Oct 11 2006
%F A038761 G.f.: (1+3*x)/(1-6*x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 03 2008]
%F A038761 a(n)=third binomial transform of 1,6,8,48,64,384 [From Al Hakanson (hawkuu(AT)gmail.com), 
               Aug 15 2009]
%p A038761 a[0]:=1: a[1]:=9: for n from 2 to 26 do a[n]:=6*a[n-1]-a[n-2] od: seq(a[n], 
               n=0..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 26 
               2006
%Y A038761 Cf. A038762.
%Y A038761 Sequence in context: A055854 A122588 A005025 this_sequence A003698 A001688 
               A144040
%Y A038761 Adjacent sequences: A038758 A038759 A038760 this_sequence A038762 A038763 
               A038764
%K A038761 easy,nonn
%O A038761 0,2
%A A038761 Barry E. Williams, May 02 2000
%E A038761 More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 04 2000

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