A104896 a(0) = 0; a(n) = 7*a(n-1) + 7.

0, 7, 56, 399, 2800, 19607, 137256, 960799, 6725600, 47079207, 329554456, 2306881199, 16148168400, 113037178807, 791260251656, 5538821761599, 38771752331200, 271402266318407, 1899815864228856, 13298711049601999, 93090977347214000, 651636841430498007

Offset: 0

Author

Alexandre Wajnberg, Apr 24 2005

Keywords

• easy
• nonn

Comments

Conjecture: this is also the number of integers from 0 to 10^n - 1 that lack 0, 1 and 2 as a digit.

Number of monic irreducible polynomials of degree 1 in GF(7)[x1,...,xn]. - Max Alekseyev, Jan 23 2006

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (8,-7).

Crossrefs

Cf. A000918, A029858, A052379, A052386, A080674.

Row n=7 of A228275.

Programs

Magma

[(7/6)*(7^n -1): n in [0..30]]; // G. C. Greubel, Jun 09 2021

Maple

a:=n->sum (7^j,j=1..n): seq(a(n), n=0..30); # Zerinvary Lajos, Oct 03 2007

Mathematica

RecurrenceTable[{a[n]==7*a[n-1]+7,a[0]==0},a,{n,0,30}] (* Vaclav Kotesovec, Jul 25 2014 *)

PARI

concat(0, Vec(7*x/((x-1)*(7*x-1)) + O(x^30))) \\ Colin Barker, Jul 25 2014

Sage

[(7/6)*(7^n -1) for n in (0..30)] # G. C. Greubel, Jun 09 2021

Formula

a(n) = (7^(n+1) - 7) / 6. - Max Alekseyev, Jan 23 2006

a(n) = a(n-1) + 7^n with a(0)=0. - Vincenzo Librandi, Nov 13 2010

From Colin Barker, Jul 25 2014: (Start)

a(n) = 8*a(n-1) - 7*a(n-2).

G.f.: 7*x / ((x-1)*(7*x-1)). (End)

E.g.f.: (7/6)*(exp(7*x) - exp(x)). - G. C. Greubel, Jun 09 2021