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A099672
Partial sums of repdigits of A002279.
1
5, 60, 615, 6170, 61725, 617280, 6172835, 61728390, 617283945, 6172839500, 61728395055, 617283950610, 6172839506165, 61728395061720, 617283950617275, 6172839506172830, 61728395061728385, 617283950617283940, 6172839506172839495, 61728395061728395050
OFFSET
1,1
FORMULA
a(n) = (5/81)*(10^(n+1) - 9*n - 10). - R. Piyo (nagoya314(AT)yahoo.com), Dec 10 2004.
From Colin Barker, Nov 30 2017: (Start)
G.f.: 5*x / ((1 - x)^2*(1 - 10*x)).
a(n) = 12*a(n-1) - 21*a(n-2) + 10*a(n-3) for n>2.
(End)
EXAMPLE
5 + 55 + 555 + 5555 + 55555 = a(5) = 61725.
MATHEMATICA
<<NumberTheory`NumberTheoryFunctions` Table[{k, Table[Apply[Plus, Table[k*(10^n-1)/9, {n, 1, m}]], {m, 1, 35}]}, {k, 1, 9}]
Table[5/9*Sum[10^i - 1, {i, n}], {n, 18}] (* Robert G. Wilson v, Nov 20 2004 *)
Accumulate[Table[FromDigits[PadRight[{}, n, 5]], {n, 0, 20}]] (* Harvey P. Dale, Oct 05 2013 *)
PROG
(PARI) Vec(5*x / ((1 - x)^2*(1 - 10*x)) + O(x^40)) \\ Colin Barker, Nov 30 2017
CROSSREFS
KEYWORD
base,nonn,easy
AUTHOR
Labos Elemer, Nov 17 2004
STATUS
approved