Search: id:A079291
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%I A079291
%S A079291 0,1,4,25,144,841,4900,28561,166464,970225,5654884,32959081,192099600,
%T A079291 1119638521,6525731524,38034750625,221682772224,1292061882721,
%U A079291 7530688524100,43892069261881,255821727047184,1491038293021225
%N A079291 Squares of Pell numbers.
%C A079291 a(n)*(-1)^(n+1) is the r=-4 member of the r-family of sequences S_r(n), 
               n>=1, defined in A092184 where more information can be found.
%H A079291 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 A079291 P. Stanica, <a href="http://arXiv.org/abs/math.CO/0010149">Generating 
               functions, weighted and non-weighted sums of powers...</a>
%H A079291 T. Mansour, <a href="http://arXiv.org/abs/math.CO/0303138">Squaring the 
               terms of an ell-th order linear recurrence</a>
%H A079291 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A079291 G.f.: x*(1-x)/(1+x)/(1-6x+x^2). a(n)=(r^n+(1/r)^n-2*(-1)^n)/8, with r=3+sqrt(8). 
               a(n+3)=5*a(n+2)+5*a(n+1)-a(n).
%F A079291 a(n+1) = sum_{k=0...n}((-1)^(n-k)*A001653(k)); e.g. 144 = -1 + 5 - 29 
               + 169; 25 = 1 - 5 + 29 - Charlie Marion (charliem(AT)bestweb.net), 
               Jul 16 2003
%F A079291 a(n)=A000129(n)^2.
%F A079291 a(n)= (T(n, 3)-(-1)^n)/4 with Chebyshev's polynomials of the first kind 
               evaluated at x=3: T(n, 3)=A001541(n)=((3+2*sqrt(2))^n + (3-2*sqrt(2))^n)/
               2. W. Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), 
               Oct 18 2004
%F A079291 a(n) = rightmost term of M^n * [1 0 0] where M = the 3 X 3 matrix [4 
               4 1 / 2 1 0 / 1 0 0]. a(n+1) = leftmost term. E.g. a(6) = 4900, a(5) 
               = 841 since M^5 * [1 0 0] = [4900 2030 841]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Oct 31 2004
%F A079291 a(n) = [(-1)^(n+1)+A001109(n+1)-3*A001109(n)]/4. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Nov 16 2007
%F A079291 a(n) = ( ( ( (1-Sqrt[ 2 ])^n + (1+Sqrt[ 2 ])^n) /2 )^2 + (-1)^(n+1) ) 
               /2 - Antonio Pane (apane1(AT)spc.edu), Dec 15 2007
%p A079291 with(combinat):seq(fibonacci(i,2)^2,i=0..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 20 2008
%Y A079291 Cf. A000129.
%Y A079291 Cf. A001254, A007598.
%Y A079291 Sequence in context: A123660 A156701 A015533 this_sequence A072221 A055846 
               A091634
%Y A079291 Adjacent sequences: A079288 A079289 A079290 this_sequence A079292 A079293 
               A079294
%K A079291 easy,nonn
%O A079291 0,3
%A A079291 Ralf Stephan (ralf(AT)ark.in-berlin.de), Feb 08 2003

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