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a(n)^2 is the smallest square containing exactly n 0's.
1

%I #29 Sep 08 2022 08:44:57

%S 0,10,320,100,3200,1000,32000,10000,320000,100000,3200000,1000000,

%T 32000000,10000000,320000000,100000000,3200000000,1000000000,

%U 32000000000,10000000000,320000000000,100000000000

%N a(n)^2 is the smallest square containing exactly n 0's.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SquareNumber.html">Square Number</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,10).

%F From _Ralf Stephan_, Jul 18 2013: (Start)

%F a(n) = 10*a(n-2); a(0)=0, a(1)=10, a(2)=320.

%F G.f.: (10*x + 320*x^2)/(1-10*x^2). (End)

%t LinearRecurrence[{0,10},{0,10,320},30] (* _Harvey P. Dale_, Feb 10 2022 *)

%o (Magma) a:=[0,10,320]; [n le 3 select a[n] else 10*Self(n-2):n in [1..25]]; // _Marius A. Burtea_, Oct 11 2019

%Y Cf. A000290, A036507.

%K nonn,base,easy

%O 1,2

%A _Patrick De Geest_, Mar 15 1999

%E More terms from _Lior Manor_, Jul 02 2001

%E a(20) corrected by _Georg Fischer_, Dec 07 2019