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a(0) = 0; a(n) = 7*a(n-1) + 7.
3

%I #31 Sep 08 2022 08:45:17

%S 0,7,56,399,2800,19607,137256,960799,6725600,47079207,329554456,

%T 2306881199,16148168400,113037178807,791260251656,5538821761599,

%U 38771752331200,271402266318407,1899815864228856,13298711049601999,93090977347214000,651636841430498007

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

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

%C Number of monic irreducible polynomials of degree 1 in GF(7)[x1,...,xn]. - _Max Alekseyev_, Jan 23 2006

%H Alois P. Heinz, <a href="/A104896/b104896.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-7).

%F a(n) = (7^(n+1) - 7) / 6. - _Max Alekseyev_, Jan 23 2006

%F a(n) = a(n-1) + 7^n with a(0)=0. - _Vincenzo Librandi_, Nov 13 2010

%F From _Colin Barker_, Jul 25 2014: (Start)

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

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

%F E.g.f.: (7/6)*(exp(7*x) - exp(x)). - _G. C. Greubel_, Jun 09 2021

%p a:=n->sum (7^j,j=1..n): seq(a(n), n=0..30); # _Zerinvary Lajos_, Oct 03 2007

%t RecurrenceTable[{a[n]==7*a[n-1]+7,a[0]==0},a,{n,0,30}] (* _Vaclav Kotesovec_, Jul 25 2014 *)

%o (PARI) concat(0, Vec(7*x/((x-1)*(7*x-1)) + O(x^30))) \\ _Colin Barker_, Jul 25 2014

%o (Magma) [(7/6)*(7^n -1): n in [0..30]]; // _G. C. Greubel_, Jun 09 2021

%o (Sage) [(7/6)*(7^n -1) for n in (0..30)] # _G. C. Greubel_, Jun 09 2021

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

%Y Row n=7 of A228275.

%K easy,nonn

%O 0,2

%A _Alexandre Wajnberg_, Apr 24 2005