Search: id:A054490
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%I A054490
%S A054490 1,11,65,379,2209,12875,75041,437371,2549185,14857739,86597249,
%T A054490 504725755,2941757281,17145817931,99933150305,582453083899,
%U A054490 3394785353089,19786259034635,115322768854721,672150354093691
%N A054490 A Pellian-related second order recursive sequence.
%C A054490 Additionally, (A054490)=sqrt{8*(A038723)^2-7}
%D A054490 I. Adler, Three Diophantine equations - Part II, Fib. Quart., 7(1969), 
               pps. 181-193.
%D A054490 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N. Y., 1964, 
               pps. 122-125, 194-196.
%D A054490 E. I. Emerson, Recurrent Sequences in the Equation DQ^2=R^2+N, Fib. Quart., 
               7(1969), pps. 231-242.
%H A054490 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A054490 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A054490 a(n)=6a(n-1)-a(n-2), a(0)=1, a(1)=11.
%F A054490 a(n)={11*([3+2sqrt(2)]^n-[3-2sqrt(2)]^n)-([3+2sqrt(2)]^(n-1)-[3-2sqrt(2)]^(n-1))}/
               4sqrt(2).
%F A054490 G.f.: (1+5*x)/(1-6*x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 03 2008]
%F A054490 a(n)=third binomial transform of 1,8,8,64,64,512 [From Al Hakanson (hawkuu(AT)gmail.com), 
               Aug 17 2009]
%e A054490 a(3)=379 [From Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009]
%p A054490 a[0]:=1: a[1]:=11: 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 A054490 Cf. A054488, A054489, A038723.
%Y A054490 Sequence in context: A054333 A036601 A125321 this_sequence A126479 A139611 
               A154617
%Y A054490 Adjacent sequences: A054487 A054488 A054489 this_sequence A054491 A054492 
               A054493
%K A054490 easy,nonn
%O A054490 0,2
%A A054490 Barry E. Williams, May 04 2000
%E A054490 More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 05 2000

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