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A125687 The base 6 numbers 4 44 444 4444 44444 ... converted to base 10.

%I A125687 #21 Mar 29 2025 09:15:35
%S A125687 4,28,172,1036,6220,37324,223948,1343692,8062156,48372940,290237644,
%T A125687 1741425868,10448555212,62691331276,376147987660,2256887925964,
%U A125687 13541327555788,81247965334732,487487792008396,2924926752050380,17549560512302284,105297363073813708,631784178442882252
%N A125687 The base 6 numbers 4 44 444 4444 44444 ... converted to base 10.
%H A125687 Harvey P. Dale, <a href="/A125687/b125687.txt">Table of n, a(n) for n = 1..1000</a>
%H A125687 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,-6).
%F A125687 a(n) = 4*(6^n - 1)/5.
%F A125687 G.f.: 4*x/((1-x)*(1-6*x)). - _Vincenzo Librandi_, Sep 26 2015
%F A125687 From _Elmo R. Oliveira_, Mar 29 2025: (Start)
%F A125687 E.g.f.: 4*exp(x)*(exp(5*x) - 1)/5.
%F A125687 a(n) = 4*A003464(n).
%F A125687 a(n) = 7*a(n-1) - 6*a(n-2) for n > 2. (End)
%e A125687 Base 6.........decimal
%e A125687 4....................4
%e A125687 44..................28
%e A125687 444................172
%e A125687 4444..............1036
%e A125687 44444.............6220
%e A125687 444444...........37324
%e A125687 4444444.........223948
%e A125687 44444444.......1343692
%e A125687 444444444......8062156
%e A125687 4444444444....48372940
%e A125687 etc.
%p A125687 seq((6^n-1)*4/5, n=1..24);
%t A125687 4 (6^Range[20]-1)/5  (* _Harvey P. Dale_, Mar 12 2011 *)
%t A125687 Rest[CoefficientList[Series[4 x/((1 - x) (1 - 6 x)), {x, 0, 30}], x]] (* _Vincenzo Librandi_, Sep 26 2015 *)
%t A125687 Table[FromDigits[PadRight[{},n,4],6],{n,30}] (* or *) LinearRecurrence[{7,-6},{4,28},30] (* _Harvey P. Dale_, Jan 02 2023 *)
%o A125687 (Magma) [(6^n-1)*4/5: n in [1.. 35]]; // _Vincenzo Librandi_, Sep 26 2015
%Y A125687 Cf. A003464.
%K A125687 easy,nonn
%O A125687 1,1
%A A125687 _Zerinvary Lajos_, Jan 31 2007
%E A125687 Edited by _N. J. A. Sloane_, Feb 02 2007
%E A125687 More terms from _Vincenzo Librandi_, Sep 26 2015