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A099672 Partial sums of repdigits of A002279.

%I A099672 #14 Apr 03 2025 11:50:37
%S A099672 5,60,615,6170,61725,617280,6172835,61728390,617283945,6172839500,
%T A099672 61728395055,617283950610,6172839506165,61728395061720,
%U A099672 617283950617275,6172839506172830,61728395061728385,617283950617283940,6172839506172839495,61728395061728395050,617283950617283950605
%N A099672 Partial sums of repdigits of A002279.
%H A099672 Colin Barker, <a href="/A099672/b099672.txt">Table of n, a(n) for n = 1..999</a>
%H A099672 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12,-21,10).
%F A099672 a(n) = (5/81)*(10^(n+1) - 9*n - 10). - R. Piyo (nagoya314(AT)yahoo.com), Dec 10 2004.
%F A099672 From _Colin Barker_, Nov 30 2017: (Start)
%F A099672 G.f.: 5*x/((1 - x)^2*(1 - 10*x)).
%F A099672 a(n) = 12*a(n-1) - 21*a(n-2) + 10*a(n-3) for n > 3. (End)
%F A099672 From _Elmo R. Oliveira_, Apr 03 2025: (Start)
%F A099672 E.g.f.: 5*exp(x)*(10*exp(9*x) - 9*x - 10)/81.
%F A099672 a(n) = 5*A014824(n). (End)
%e A099672 5 + 55 + 555 + 5555 + 55555 = a(5) = 61725.
%t A099672 <<NumberTheory`NumberTheoryFunctions` Table[{k, Table[Apply[Plus, Table[k*(10^n-1)/9, {n, 1, m}]], {m, 1, 35}]}, {k, 1, 9}]
%t A099672 Table[5/9*Sum[10^i - 1, {i, n}], {n, 18}] (* _Robert G. Wilson v_, Nov 20 2004 *)
%t A099672 Accumulate[Table[FromDigits[PadRight[{},n,5]],{n,0,20}]] (* _Harvey P. Dale_, Oct 05 2013 *)
%o A099672 (PARI) Vec(5*x/((1 - x)^2*(1 - 10*x)) + O(x^40)) \\ _Colin Barker_, Nov 30 2017
%Y A099672 Cf. A002275-A002283, A014824, A057932, A099669-A099675.
%K A099672 base,nonn,easy
%O A099672 1,1
%A A099672 _Labos Elemer_, Nov 17 2004