%I #19 Jun 26 2024 04:05:14

%S 5,46,452,4504,45008,450016,4500032,45000064,450000128,4500000256,

%T 45000000512,450000001024,4500000002048,45000000004096,

%U 450000000008192,4500000000016384,45000000000032768,450000000000065536,4500000000000131072,45000000000000262144

%N Number of (2n+1)-digit squares in carryless arithmetic mod 10.

%H David Applegate, Marc LeBrun and N. J. A. Sloane, <a href="http://neilsloane.com/doc/carry1.pdf">Carryless Arithmetic (I): The Mod 10 Version</a>.

%H <a href="/index/Ca#CARRYLESS">Index entries for sequences related to carryless arithmetic</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-20).

%F For formula see Maple code.

%F a(n) = 12*a(n-1)-20*a(n-2). G.f.: -(14*x-5) / ((2*x-1)*(10*x-1)). - _Colin Barker_, May 11 2013

%p f :- n->2^((n-1)/2) + add( 5^d*2^((n+1)/2),d=0..(n-3)/2) + 2^((n+3)/2)*5^((n-1)/2);

%t LinearRecurrence[{12, -20}, {5, 46}, 25] (* _Paolo Xausa_, Jun 26 2024 *)

%Y See A059729 for the actual squares.

%K nonn,base,easy

%O 0,1

%A _N. J. A. Sloane_, Aug 07 2010