Search: id:A081068
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%I A081068
%S A081068 1,4,25,169,1156,7921,54289,372100,2550409,17480761,119814916,821223649,
%T A081068 5628750625,38580030724,264431464441,1812440220361,12422650078084,
%U A081068 85146110326225,583600122205489,4000054745112196,27416783093579881
%N A081068 (Lucas(4n+2)+2)/5, or Fibonacci(2n+1)^2, or A081067/5.
%D A081068 Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and 
               Sons, 1998, p. 75
%D A081068 A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of 
               combinatorial proof, M.A.A. 2003, id. 19.
%F A081068 a(n) = 8a(n-1)-8a(n-2)+a(n-3)
%F A081068 a(n)=(2/5)+(3/10)*{[(7/2)-(3/2)*sqrt(5)]^n+[(7/2)+(3/2)*sqrt(5)]^n}+(1/
               10)*sqrt(5)*{[(7/2) +(3/2)*sqrt(5)]^n-[(7/2)-(3/2)*sqrt(5)]^n}, with 
               n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Dec 01 2008]
%p A081068 luc := proc(n) option remember: if n=0 then RETURN(2) fi: if n=1 then 
               RETURN(1) fi: luc(n-1)+luc(n-2): end: for n from 0 to 40 do printf(`%d,
               `,(luc(4*n+2)+2)/5) od:
%Y A081068 Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers), A081067.
%Y A081068 Equals A001519(n)^2 and A058038 - 1.
%Y A081068 First differences of A103433.
%Y A081068 Sequence in context: A074422 A128419 A006880 this_sequence A163072 A140177 
               A034494
%Y A081068 Adjacent sequences: A081065 A081066 A081067 this_sequence A081069 A081070 
               A081071
%K A081068 nonn,easy
%O A081068 0,2
%A A081068 R. K. Guy (rkg(AT)cpsc.ucalgary.ca), Mar 04, 2003
%E A081068 More terms and Maple code from James A. Sellers (sellersj(AT)math.psu.edu), 
               Mar 05, 2003

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