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%I #24 Sep 08 2022 08:46:08
%S 111,10111,1001111,100011111,10000111111,1000001111111,
%T 100000011111111,10000000111111111,1000000001111111111,
%U 100000000011111111111,10000000000111111111111,1000000000001111111111111,100000000000011111111111111,10000000000000111111111111111
%N Binary representation of 4^n + 2^(n+1) - 1.
%H Colin Barker, <a href="/A244663/b244663.txt">Table of n, a(n) for n = 1..450</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Kynea_number">Kynea number</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F a(n) = -1/9+10^(1+n)/9+100^n.
%F a(n) = 111*a(n-1)-1110*a(n-2)+1000*a(n-3).
%F G.f.: -x*(2000*x^2-2210*x+111) / ((x-1)*(10*x-1)*(100*x-1)).
%e a(3) is 1001111 because A093069(3) = 79 which is 1001111 in base 2.
%p A244663:=n->-1/9+10^(1+n)/9+100^n: seq(A244663(n), n=1..15); # _Wesley Ivan Hurt_, Jul 09 2014
%t Table[-1/9 + 10^(1 + n)/9 + 100^n, {n, 15}] (* _Wesley Ivan Hurt_, Jul 09 2014 *)
%t LinearRecurrence[{111,-1110,1000},{111,10111,1001111},20] (* _Harvey P. Dale_, Dec 11 2014 *)
%o (PARI) vector(100, n, -1/9+10^(1+n)/9+100^n)
%o (PARI) Vec(-x*(2000*x^2-2210*x+111)/((x-1)*(10*x-1)*(100*x-1)) + O(x^100))
%o (Magma) [-1/9 + 10^(1 + n)/9 + 100^n : n in [1..15]]; // _Wesley Ivan Hurt_, Jul 09 2014
%Y Cf. A093069.
%K nonn,easy,base
%O 1,1
%A _Colin Barker_, Jul 08 2014
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