A125823 Numbers whose base 7 representation is 4444....4.

0, 4, 32, 228, 1600, 11204, 78432, 549028, 3843200, 26902404, 188316832, 1318217828, 9227524800, 64592673604, 452148715232, 3165041006628, 22155287046400, 155087009324804, 1085609065273632, 7599263456915428, 53194844198408000, 372363909388856004, 2606547365721992032

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (8,-7).

Formula

a(n) = 2*(7^(n-1) - 1)/3 = 4*A023000(n-1).

a(n) = 7*a(n-1) + 4, with a(1)=0. - Vincenzo Librandi, Sep 30 2010

From G. C. Greubel, Aug 03 2019: (Start)

G.f.: 4*x^2/((1-x)*(1-7*x)).

E.g.f.: 2*(exp(7*x) - exp(x))/3. (End)

Example

Base 7.................decimal
0.........................0
4.........................4
44.......................32
444.....................228
4444...................1600
44444.................11204
444444................78432
4444444..............549028
44444444............3843200
etc....................etc...

Maple

seq(4*(7^n-1)/6, n=0..21);

Mathematica

2*(7^(Range[30]-1) -1)/3 (* G. C. Greubel, Aug 03 2019 *)

Prog

(PARI) vector(30, n, 2*(7^(n-1) -1)/3) \\ G. C. Greubel, Aug 03 2019
(Magma) [2*(7^(n-1) -1)/3: n in [1..30]]; // G. C. Greubel, Aug 03 2019
(Sage) [2*(7^(n-1) -1)/3 for n in (1..30)] # G. C. Greubel, Aug 03 2019
(GAP) List([1..30], n-> 2*(7^(n-1) -1)/3); # G. C. Greubel, Aug 03 2019

Crossrefs

Cf. A023000.

Sequence in context: A099269 A316810 A299656 * A320366 A317560 A302742

Adjacent sequences: A125820 A125821 A125822 * A125824 A125825 A125826

Keyword

easy,nonn

Author

Zerinvary Lajos, Feb 03 2007

Extensions

Terms a(21) onward added by G. C. Greubel, Aug 03 2019

Status

approved