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

%I A125823 #18 Sep 08 2022 08:45:28
%S A125823 0,4,32,228,1600,11204,78432,549028,3843200,26902404,188316832,
%T A125823 1318217828,9227524800,64592673604,452148715232,3165041006628,
%U A125823 22155287046400,155087009324804,1085609065273632,7599263456915428,53194844198408000,372363909388856004,2606547365721992032
%N A125823 Numbers whose base 7 representation is 4444....4.
%H A125823 G. C. Greubel, <a href="/A125823/b125823.txt">Table of n, a(n) for n = 1..1000</a>
%H A125823 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-7).
%F A125823 a(n) = 2*(7^(n-1) - 1)/3 = 4*A023000(n-1).
%F A125823 a(n) = 7*a(n-1) + 4, with a(1)=0. - _Vincenzo Librandi_, Sep 30 2010
%F A125823 From _G. C. Greubel_, Aug 03 2019: (Start)
%F A125823 G.f.: 4*x^2/((1-x)*(1-7*x)).
%F A125823 E.g.f.: 2*(exp(7*x) - exp(x))/3. (End)
%e A125823 Base 7.................decimal
%e A125823 0.........................0
%e A125823 4.........................4
%e A125823 44.......................32
%e A125823 444.....................228
%e A125823 4444...................1600
%e A125823 44444.................11204
%e A125823 444444................78432
%e A125823 4444444..............549028
%e A125823 44444444............3843200
%e A125823 etc....................etc...
%p A125823 seq(4*(7^n-1)/6, n=0..21);
%t A125823 2*(7^(Range[30]-1) -1)/3 (* _G. C. Greubel_, Aug 03 2019 *)
%o A125823 (PARI) vector(30, n, 2*(7^(n-1) -1)/3) \\ _G. C. Greubel_, Aug 03 2019
%o A125823 (Magma) [2*(7^(n-1) -1)/3: n in [1..30]]; // _G. C. Greubel_, Aug 03 2019
%o A125823 (Sage) [2*(7^(n-1) -1)/3 for n in (1..30)] # _G. C. Greubel_, Aug 03 2019
%o A125823 (GAP) List([1..30], n-> 2*(7^(n-1) -1)/3); # _G. C. Greubel_, Aug 03 2019
%Y A125823 Cf. A023000.
%K A125823 easy,nonn
%O A125823 1,2
%A A125823 _Zerinvary Lajos_, Feb 03 2007
%E A125823 Terms a(21) onward added by _G. C. Greubel_, Aug 03 2019