Search: id:A076218
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%I A076218
%S A076218 0,1,5,145,4901,166465,5654885,192099601,6525731525,221682772225,
%T A076218 7530688524101,255821727047185,8690408031080165,295218051329678401,
%U A076218 10028723337177985445,340681375412721826705,11573138040695364122501
%N A076218 Numbers n such that 2*n^2 - 3*n + 1 is a square.
%C A076218 Lim n -> Inf. a(n)/a(n-1) = 33.970562748477140585620264690516 = 17 + 
               12*Sqrt(2).
%F A076218 Formula: ( (3+(17+12*sqrt(2))^(n-1)) + (3+(17-12*sqrt(2))^(n-1)) )/8 
               for n>=1; Recurrence: a(n) = 35*(a(n-1)-a(n-2))+a(n-3) with a(1) 
               = 1, a(2) = 5, a(3) = 145; Generating function = (x-30*x^2+5*x^3)/
               (1-35*x+35*x^2-x^3). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), 
               Nov 04 2002
%F A076218 Product of adjacent odd subscripted Pell series numbers (A000129). - 
               Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 07 2003
%F A076218 Sqrt(2) - 1 = .414213562...= 2/5 + 2/145 + 2/4901 + 2/166465...= Sum 
               (2 through infinity) 2/a(n). - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Jun 07 2003
%F A076218 For n>0, one more than square of adjacent even subscripted Pell series 
               numbers (A000129). - Charlie Marion (charliemath(AT)optonline.net), 
               Mar 09 2005
%Y A076218 Sequence in context: A037049 A134503 A081322 this_sequence A075186 A113560 
               A094364
%Y A076218 Adjacent sequences: A076215 A076216 A076217 this_sequence A076219 A076220 
               A076221
%K A076218 nonn
%O A076218 1,3
%A A076218 Gregory V. Richardson (omomom(AT)hotmail.com), Nov 03 2002

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