%I A091761
%S A091761 0,1,34,1155,39236,1332869,45278310,1538129671,52251130504,
%T A091761 1775000307465,60297759323306,2048348816684939,69583562007964620,
%U A091761 2363792759454112141,80299370259431848174,2727814796061228725775
%N A091761 Pell(4n)/Pell(4).
%C A091761 A000129(kn)/A000129(k)=((sqrt(2)-1)^k(-1)^k-(sqrt(2)+1)^k)((sqrt(2)-1)^(kn)(-1)^(kn)-(sqrt(2)+1)^(kn))/
               ((sqrt(2)-1)^(2k)+(sqrt(2)+1)^(2k)-2(-1)^k)
%C A091761 All squares of the form (3m-1)^3 + (3m)^3 + (3m+1)^3 (cf. A116108) are 
               given for m = 24 b, where b is a square of this sequence. From Ribenboim 
               & McDaniel, it follows there are no squares > 1 in this sequence. 
               - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Jun 05 2007
%D A091761 Paulo Ribenboim and Wayne L. McDaniel: "The Square Terms in Lucas Sequences", 
               Journal of Number Theory 58, 104-123 (1996).
%H A091761 M. F. Hasler, <a href="b091761.txt">Table of n, a(n) for n = 0..99</a>
%H A091761 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A091761 G.f.: x/(1-34x+x^2); a(n)=A000129(4n)/A000129(4); a(n)=((1+sqrt(2))^(4n)-(1-sqrt(2))^(4n))sqrt(2)/
               48.
%F A091761 a(n) = n (mod 2^m) for any m>=0. a(n) = sinh(4n*log(sqrt(2)+1)/(12 sqrt(2)) 
               a(n) = A[1,1], first element of the 2 X 2 matrix A = (34,1;-1,0)^(n-1) 
               - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Jun 05 2007
%F A091761 a(n)=34*a(n-1)-a(n-2); a(0)=0, a(1)=1. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 03 2008]
%p A091761 with (combinat):seq(fibonacci(4*n,2)/12, n=0..17); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Apr 21 2008
%o A091761 (PARI) A091761(n, x=[ -1,17],A=[17,72*4;1,17]) = vector(n,i,(x*=A)[1]) 
               - M. F. Hasler, May 26 2007
%o A091761 (PARI) A091761(n)=([34,1;-1,0]^(n-1))[1,1] - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), 
               Jun 05 2007
%o A091761 (Other) sage: [lucas_number1(n,34,1) for n in xrange(0, 16)]# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Nov 07 2009]
%Y A091761 A029547 is an essentially identical sequence.
%Y A091761 Cf. A001109, A041085, A116108.
%Y A091761 Sequence in context: A075292 A158696 A029547 this_sequence A009978 A041545 
               A167258
%Y A091761 Adjacent sequences: A091758 A091759 A091760 this_sequence A091762 A091763 
               A091764
%K A091761 easy,nonn,new
%O A091761 0,3
%A A091761 Paul Barry (pbarry(AT)wit.ie), Feb 06 2004