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%I #21 Feb 04 2023 12:27:03
%S 0,3,18,93,468,2343,11718,58593,292968,1464843,7324218,36621093,
%T 183105468,915527343,4577636718,22888183593,114440917968,572204589843,
%U 2861022949218,14305114746093,71525573730468,357627868652343
%N Numbers whose base-5 representation is 333333.......3.
%H G. C. Greubel, <a href="/A125833/b125833.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-5).
%F a(n) = 3*(5^n - 1)/4.
%F a(n) = 5*a(n-1) + 3 for n > 0, a(0)=0. - _Vincenzo Librandi_, Sep 30 2010
%F From _G. C. Greubel_, Aug 03 2019: (Start)
%F a(n) = 3*A003463(n).
%F G.f.: 3*x/((1-x)*(1-5*x)).
%F E.g.f.: 3*(exp(5*x) - exp(x))/4. (End)
%e Base 5.................decimal
%e 0.........................0
%e 3.........................3
%e 33.......................18
%e 333......................93
%e 3333....................468
%e 33333..................2343
%e 333333................11718
%e 3333333...............58593
%e 33333333.............292968, etc.
%p seq(3*(5^n-1)/4, n=0..30);
%t Table[FromDigits[PadRight[{},n,3],5],{n,0,30}] (* or *) LinearRecurrence[ {6,-5},{0,3},30] (* _Harvey P. Dale_, Sep 23 2016 *)
%t 3*(5^Range[0,30] -1)/4 (* _G. C. Greubel_, Aug 03 2019 *)
%o (PARI) vector(30, n, n--; 3*(5^n -1)/4) \\ _G. C. Greubel_, Aug 03 2019
%o (Magma) [3*(5^n -1)/4: n in [0..30]]; // _G. C. Greubel_, Aug 03 2019
%o (Sage) [3*(5^n -1)/4 for n in (0..30)] # _G. C. Greubel_, Aug 03 2019
%o (GAP) List([0..30], n-> 3*(5^n -1)/4); _G. C. Greubel_, Aug 03 2019
%Y Cf. A003463.
%K nonn,easy
%O 0,2
%A _Zerinvary Lajos_, Feb 03 2007
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