Search: id:A124124
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%I A124124
%S A124124 1,2,6,13,37,78,218,457,1273,2666,7422,15541,43261,90582,252146,527953,
%T A124124 1469617,3077138,8565558
%N A124124 Nonnegative integers n such that 2n^2+2n-3 is square.
%C A124124 For squares of the form 2n^2-2n-3, the answer is b(n) = 1 + a(n). - Zak 
               Seidov Dec 04 2006.
%C A124124 First differences are apparently in A143608. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jul 17 2009]
%F A124124 It appears that a(n)=2a(n-1)-2a(n-2)+a(n-3) if n is even, a(n)=5a(n-1)-5a(n-2)+a(n-3) 
               if n is odd. Can anyone confirm this?
%F A124124 Yes, these formulae are correct. Also a(i) = 7*(a(i-2) - a(i-4)) + a(i-6) 
               for i >= 7. - Zak Seidov Dec 04 2006
%F A124124 2*a(n)=sqrt[7+2*A077442(n-1)^2]-1. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Dec 03 2006
%F A124124 a(n)=a(n-1)+6*a(n-2)-6*a(n-3)-a(n-4)+a(n-5). G.f.: -x*(1+x-2*x^2+x^3+x^4)/
               ((x-1)*(x^2-2*x-1)*(x^2+2*x-1)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jul 17 2009]
%Y A124124 Cf. A001108, A046172, A008844.
%Y A124124 Sequence in context: A116426 A162057 A026550 this_sequence A052450 A001373 
               A057243
%Y A124124 Adjacent sequences: A124121 A124122 A124123 this_sequence A124125 A124126 
               A124127
%K A124124 nonn
%O A124124 1,2
%A A124124 John W. Layman (layman(AT)math.vt.edu), Nov 29 2006

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