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

4, 28, 172, 1036, 6220, 37324, 223948, 1343692, 8062156, 48372940, 290237644, 1741425868, 10448555212, 62691331276, 376147987660, 2256887925964, 13541327555788, 81247965334732, 487487792008396, 2924926752050380, 17549560512302284, 105297363073813708, 631784178442882252

Offset: 1

Author

Zerinvary Lajos, Jan 31 2007

Keywords

• easy
• nonn

Examples

			Base 6.........decimal
4....................4
44..................28
444................172
4444..............1036
44444.............6220
444444...........37324
4444444.........223948
44444444.......1343692
444444444......8062156
4444444444....48372940
etc.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-6).

Crossrefs

Cf. A003464.

Programs

Magma

[(6^n-1)*4/5: n in [1.. 35]]; // Vincenzo Librandi, Sep 26 2015

Maple

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

Mathematica

4 (6^Range[20]-1)/5  (* Harvey P. Dale, Mar 12 2011 *)
Rest[CoefficientList[Series[4 x/((1 - x) (1 - 6 x)), {x, 0, 30}], x]] (* Vincenzo Librandi, Sep 26 2015 *)
Table[FromDigits[PadRight[{},n,4],6],{n,30}] (* or *) LinearRecurrence[{7,-6},{4,28},30] (* Harvey P. Dale, Jan 02 2023 *)

Formula

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

G.f.: 4*x/((1-x)*(1-6*x)). - Vincenzo Librandi, Sep 26 2015

From Elmo R. Oliveira, Mar 29 2025: (Start)

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

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

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

Extensions

Edited by N. J. A. Sloane, Feb 02 2007

More terms from Vincenzo Librandi, Sep 26 2015