%I #21 Mar 29 2025 09:15:35

%S 4,28,172,1036,6220,37324,223948,1343692,8062156,48372940,290237644,

%T 1741425868,10448555212,62691331276,376147987660,2256887925964,

%U 13541327555788,81247965334732,487487792008396,2924926752050380,17549560512302284,105297363073813708,631784178442882252

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

%H Harvey P. Dale, <a href="/A125687/b125687.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,-6).

%F a(n) = 4*(6^n - 1)/5.

%F G.f.: 4*x/((1-x)*(1-6*x)). - _Vincenzo Librandi_, Sep 26 2015

%F From _Elmo R. Oliveira_, Mar 29 2025: (Start)

%F E.g.f.: 4*exp(x)*(exp(5*x) - 1)/5.

%F a(n) = 4*A003464(n).

%F a(n) = 7*a(n-1) - 6*a(n-2) for n > 2. (End)

%e Base 6.........decimal

%e 4....................4

%e 44..................28

%e 444................172

%e 4444..............1036

%e 44444.............6220

%e 444444...........37324

%e 4444444.........223948

%e 44444444.......1343692

%e 444444444......8062156

%e 4444444444....48372940

%e etc.

%p seq((6^n-1)*4/5, n=1..24);

%t 4 (6^Range[20]-1)/5 (* _Harvey P. Dale_, Mar 12 2011 *)

%t Rest[CoefficientList[Series[4 x/((1 - x) (1 - 6 x)), {x, 0, 30}], x]] (* _Vincenzo Librandi_, Sep 26 2015 *)

%t Table[FromDigits[PadRight[{},n,4],6],{n,30}] (* or *) LinearRecurrence[{7,-6},{4,28},30] (* _Harvey P. Dale_, Jan 02 2023 *)

%o (Magma) [(6^n-1)*4/5: n in [1.. 35]]; // _Vincenzo Librandi_, Sep 26 2015

%Y Cf. A003464.

%K easy,nonn

%O 1,1

%A _Zerinvary Lajos_, Jan 31 2007

%E Edited by _N. J. A. Sloane_, Feb 02 2007

%E More terms from _Vincenzo Librandi_, Sep 26 2015