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%I #11 Nov 30 2017 10:42:41
%S 5,60,615,6170,61725,617280,6172835,61728390,617283945,6172839500,
%T 61728395055,617283950610,6172839506165,61728395061720,
%U 617283950617275,6172839506172830,61728395061728385,617283950617283940,6172839506172839495,61728395061728395050
%N Partial sums of repdigits of A002279.
%H Colin Barker, <a href="/A099672/b099672.txt">Table of n, a(n) for n = 1..999</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12,-21,10).
%F a(n) = (5/81)*(10^(n+1) - 9*n - 10). - R. Piyo (nagoya314(AT)yahoo.com), Dec 10 2004.
%F From _Colin Barker_, Nov 30 2017: (Start)
%F G.f.: 5*x / ((1 - x)^2*(1 - 10*x)).
%F a(n) = 12*a(n-1) - 21*a(n-2) + 10*a(n-3) for n>2.
%F (End)
%e 5 + 55 + 555 + 5555 + 55555 = a(5) = 61725.
%t <<NumberTheory`NumberTheoryFunctions` Table[{k, Table[Apply[Plus, Table[k*(10^n-1)/9, {n, 1, m}]], {m, 1, 35}]}, {k, 1, 9}]
%t Table[5/9*Sum[10^i - 1, {i, n}], {n, 18}] (* _Robert G. Wilson v_, Nov 20 2004 *)
%t Accumulate[Table[FromDigits[PadRight[{},n,5]],{n,0,20}]] (* _Harvey P. Dale_, Oct 05 2013 *)
%o (PARI) Vec(5*x / ((1 - x)^2*(1 - 10*x)) + O(x^40)) \\ _Colin Barker_, Nov 30 2017
%Y Cf. A057932, A002275-A002283, A099669-A099675.
%K base,nonn,easy
%O 1,1
%A _Labos Elemer_, Nov 17 2004
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