A099670 Partial sums of repdigits of A002277.
3, 36, 369, 3702, 37035, 370368, 3703701, 37037034, 370370367, 3703703700, 37037037033, 370370370366, 3703703703699, 37037037037032, 370370370370365, 3703703703703698, 37037037037037031, 370370370370370364, 3703703703703703697, 37037037037037037030, 370370370370370370363
Offset: 1
Examples
3 + 33 + 333 + 3333 = a(4) = 3702.
Links
- Index entries for linear recurrences with constant coefficients, signature (12,-21,10).
Programs
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Maple
a:=n->sum((10^(n-j)-1^(n-j))/3,j=0..n): seq(a(n), n=1..18); # Zerinvary Lajos, Jan 15 2007
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Mathematica
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Formula
a(n) = (3/81)*(10^(n+1) - 9*n - 10). - R. Piyo (nagoya314(AT)yahoo.com), Dec 10 2004
From Elmo R. Oliveira, Apr 02 2025: (Start)
G.f.: 3*x/((1 - x)^2*(1 - 10*x)).
E.g.f.: 3*exp(x)*(10*exp(9*x) - 9*x - 10)/81.
a(n) = 3*A014824(n).
a(n) = 12*a(n-1) - 21*a(n-2) + 10*a(n-3) for n > 3. (End)
Extensions
More terms from Elmo R. Oliveira, Apr 02 2025