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A004663 Powers of 3 written in base 9.

%I A004663 #30 Mar 31 2023 17:08:20
%S A004663 1,3,10,30,100,300,1000,3000,10000,30000,100000,300000,1000000,
%T A004663 3000000,10000000,30000000,100000000,300000000,1000000000,3000000000,
%U A004663 10000000000,30000000000,100000000000,300000000000,1000000000000,3000000000000,10000000000000,30000000000000
%N A004663 Powers of 3 written in base 9.
%H A004663 Robert Israel, <a href="/A004663/b004663.txt">Table of n, a(n) for n = 0..1997</a>
%H A004663 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,10).
%F A004663 From _Paul Barry_, Jul 14 2004: (Start)
%F A004663 G.f.: (1 + 3*x)/(1 - 10*x^2);
%F A004663 a(n) = 2*a(n-1) + 3*a(n-2) + 10^floor((n-2)/2);
%F A004663 a(n) = Sum_{k=0..floor(n/2)} binomial(floor(n/2), k)*3^(n-2*k). (End)
%F A004663 a(n) = 3*a(n-1) + ((1 + (-1)^n)/2)*a(n-2) with a(0)=1, a(1)=3. - _Taras Goy_, Mar 20 2019
%F A004663 E.g.f.: cosh(sqrt(10)*x) + 3*sinh(sqrt(10)*x)/sqrt(10). - _Stefano Spezia_, Mar 31 2023
%p A004663 seq(op([10^i,3*10^i]),i=0..100); # _Robert Israel_, Jun 25 2018
%t A004663 Table[FromDigits[IntegerDigits[3^n, 9]], {n, 0, 100}] (* _G. C. Greubel_, Oct 12 2018 *)
%o A004663 (PARI) a(n)=3^bittest(n,0)*10^(n\2) \\ _M. F. Hasler_, Jun 25 2018
%Y A004663 Cf. A026383, A016116.
%Y A004663 Cf. A000244, A004656, A004658, A004659, ... : powers of 3 in base 10, 2, 4, 5, ...
%Y A004663 Cf. A000079, A004642, ..., A004655: powers of 2 written in base 10, 2, 3, ..., 16.
%K A004663 nonn,base,easy
%O A004663 0,2
%A A004663 _N. J. A. Sloane_