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

%I A104896 #31 Sep 08 2022 08:45:17
%S A104896 0,7,56,399,2800,19607,137256,960799,6725600,47079207,329554456,
%T A104896 2306881199,16148168400,113037178807,791260251656,5538821761599,
%U A104896 38771752331200,271402266318407,1899815864228856,13298711049601999,93090977347214000,651636841430498007
%N A104896 a(0) = 0; a(n) = 7*a(n-1) + 7.
%C A104896 Conjecture: this is also the number of integers from 0 to 10^n - 1 that lack 0, 1 and 2 as a digit.
%C A104896 Number of monic irreducible polynomials of degree 1 in GF(7)[x1,...,xn]. - _Max Alekseyev_, Jan 23 2006
%H A104896 Alois P. Heinz, <a href="/A104896/b104896.txt">Table of n, a(n) for n = 0..500</a>
%H A104896 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-7).
%F A104896 a(n) = (7^(n+1) - 7) / 6. - _Max Alekseyev_, Jan 23 2006
%F A104896 a(n) = a(n-1) + 7^n with a(0)=0. - _Vincenzo Librandi_, Nov 13 2010
%F A104896 From _Colin Barker_, Jul 25 2014: (Start)
%F A104896 a(n) = 8*a(n-1) - 7*a(n-2).
%F A104896 G.f.: 7*x / ((x-1)*(7*x-1)). (End)
%F A104896 E.g.f.: (7/6)*(exp(7*x) - exp(x)). - _G. C. Greubel_, Jun 09 2021
%p A104896 a:=n->sum (7^j,j=1..n): seq(a(n), n=0..30); # _Zerinvary Lajos_, Oct 03 2007
%t A104896 RecurrenceTable[{a[n]==7*a[n-1]+7,a[0]==0},a,{n,0,30}] (* _Vaclav Kotesovec_, Jul 25 2014 *)
%o A104896 (PARI) concat(0, Vec(7*x/((x-1)*(7*x-1)) + O(x^30))) \\ _Colin Barker_, Jul 25 2014
%o A104896 (Magma) [(7/6)*(7^n -1): n in [0..30]]; // _G. C. Greubel_, Jun 09 2021
%o A104896 (Sage) [(7/6)*(7^n -1) for n in (0..30)] # _G. C. Greubel_, Jun 09 2021
%Y A104896 Cf. A000918, A029858, A052379, A052386, A080674.
%Y A104896 Row n=7 of A228275.
%K A104896 easy,nonn
%O A104896 0,2
%A A104896 _Alexandre Wajnberg_, Apr 24 2005