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%I #24 Feb 23 2024 07:29:13
%S 1,4,33,200,1361,8844,58513,384400,2532321,16664084,109705793,
%T 722112600,4753448881,31289709724,205967469873,1355794944800,
%U 8924626767041,58747021129764,386706739558753,2545526317441000
%N a(n) = 4*a(n-1) + 17*a(n-2), a(1)=1, a(2)=4.
%C This is one of only two Lucas-type sequences whose 8th term is a square.
%C The other one is A006131. - _Michel Marcus_, Dec 07 2012
%H A. Bremner and N. Tzanakis, <a href="http://www.arXiv.org/abs/math.NT/0408371">Lucas sequences whose 8th term is a square</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,17).
%F G.f.: 1/(1-4x-17x^2).
%p f:= gfun:-rectoproc({a(n) = 4*a(n-1) + 17*a(n-2), a(1)=1, a(2)=4}, a(n), remember): map(f, [$0..20]); # _Georg Fischer_, Jun 18 2021
%o (Maxima)
%o a[0]:0$
%o a[1]:1$
%o a[n]:=4*a[n-1] + 17*a[n-2]$
%o A097705(n):=a[n]$
%o makelist(A097705(n),n,1,30); /* _Martin Ettl_, Nov 03 2012 */
%Y Cf. A006131.
%K nonn,easy
%O 1,2
%A _Ralf Stephan_, Aug 27 2004
%E Definition adapted to offset by _Georg Fischer_, Jun 18 2021
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