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%I #24 Sep 08 2022 08:44:35
%S 1,4,1,4,9,4,9,16,9,16,25,16,25,36,25,36,49,36,49,64,49,64,81,64,81,
%T 100,81,100,121,100,121,144,121,144,169,144,169,196,169,196,225,196,
%U 225,256,225,256,289,256,289,324,289,324,361,324,361,400,361,400,441
%N A Kutz sequence.
%H Vincenzo Librandi, <a href="/A007891/b007891.txt">Table of n, a(n) for n = 1..10000</a>
%H R. E. Kutz, <a href="http://www.jstor.org/stable/3027304">Two unusual sequences</a>, Two-Year College Mathematics Journal, 12 (1981), 316-319.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,-2,0,-1,1).
%F a(n) = (n-2*floor(n/3))^2. - _Arkadiusz Wesolowski_, Sep 28 2011
%F From _Colin Barker_, Aug 05 2016: (Start)
%F a(n) = a(n-1)+2*a(n-3)-2*a(n-4)-a(n-6)+a(n-7) for n>7.
%F G.f.: x*(1+3*x-3*x^2+x^3-x^4+x^5) / ((1-x)^3*(1+x+x^2)^2).
%F (End)
%t Table[(n - 2*Floor[n/3])^2, {n, 60}] (* _Arkadiusz Wesolowski_, Sep 29 2011 *)
%o (Magma) [(n-2*Floor(n/3))^2: n in [1..60]]; // _Vincenzo Librandi_, Sep 30 2011
%o (PARI) a(n)=(n-n\3*2)^2 \\ _Charles R Greathouse IV_, Aug 05 2016
%o (PARI) Vec(x*(1+3*x-3*x^2+x^3-x^4+x^5)/((1-x)^3*(1+x+x^2)^2) + O(x^60)) \\ _Colin Barker_, Aug 05 2016
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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