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

Author

Zerinvary Lajos, Feb 03 2007

Keywords

• easy
• nonn

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-7).

Crossrefs

Cf. A023000.

Programs

GAP

List([1..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

Maple

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

Mathematica

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

PARI

vector(30, n, 2*(7^(n-1) -1)/3) \\ G. C. Greubel, Aug 03 2019

Sage

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

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)

Extensions

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