Search: id:A001254
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%I A001254
%S A001254 4,1,9,16,49,121,324,841,2209,5776,15129,39601,103684,271441,710649,
%T A001254 1860496,4870849,12752041,33385284,87403801,228826129,599074576,
%U A001254 1568397609,4106118241,10749957124,28143753121,73681302249
%N A001254 Squares of Lucas numbers.
%D A001254 Thomas Koshy, "Fibonacci and Lucas Numbers and Applications", Wiley, 
               New York, 2001.
%D A001254 A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of 
               combinatorial proof, M.A.A. 2003, id. 36,60.
%H A001254 T. D. Noe, <a href="b001254.txt">Table of n, a(n) for n=0..200</a>
%H A001254 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A001254 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A001254 T. Mansour, <a href="http://arXiv.org/abs/math.CO/0302015">A note on 
               sum of k-th power of Horadam's sequence</a>
%H A001254 P. Stanica, <a href="http://arXiv.org/abs/math.CO/0010149">Generating 
               functions, weighted and non-weighted sums of powers...</a>
%F A001254 G.f.: g(x)=(4-7x-x^2)/(1-2x-2x^2+x^3). - Len Smiley (smiley(AT)math.uaa.alaska.edu), 
               Nov 30 2001
%F A001254 a(n)=r^n+(1/r)^n+2*(-1)^n, with r=(3+sqrt(5))/2. a(n+3)=2*a(n+2)+2*a(n+1)-a(n). 
               - Ralf Stephan (ralf(AT)ark.in-berlin.de), Feb 08 2003
%F A001254 a(n) = L(2n) + 2(-1)^n = L(n-1)*L(n+1) + 5(-1)^n.
%Y A001254 Cf. A000032, A000204.
%Y A001254 Cf. A007598, A079291.
%Y A001254 With alternating signs, cf. A075150.
%Y A001254 Bisection of A001638 and A006499. First differences of A005970.
%Y A001254 Second row of array A103324.
%Y A001254 Sequence in context: A158199 A091885 A069606 this_sequence A075150 A143763 
               A128626
%Y A001254 Adjacent sequences: A001251 A001252 A001253 this_sequence A001255 A001256 
               A001257
%K A001254 nonn,easy
%O A001254 0,1
%A A001254 N. J. A. Sloane (njas(AT)research.att.com).

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