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A117727
Partial sums of A051109.
3
1, 3, 8, 18, 38, 88, 188, 388, 888, 1888, 3888, 8888, 18888, 38888, 88888, 188888, 388888, 888888, 1888888, 3888888, 8888888, 18888888, 38888888, 88888888, 188888888, 388888888, 888888888, 1888888888, 3888888888, 8888888888
OFFSET
0,2
FORMULA
a(n) = Sum_{j=0..n} A051109(j).
From G. C. Greubel, Jul 23 2023: (Start)
a(n) = (1/9)*( -8 + 17*b(n) + 35*b(n-1) + 80*b(n-2) ), where b(n) = 10^floor(n/3)*floor((n-1 mod 3)/2).
a(n) = a(n-1) + 10*a(n-3) - 10*a(n-4).
G.f.: (1 + 2*x + 5*x^2)/((1 - x)*(1 - 10*x^3)). (End)
MATHEMATICA
LinearRecurrence[{1, 0, 10, -10}, {1, 3, 8, 18}, 41] (* G. C. Greubel, Jul 23 2023 *)
PROG
(Magma) I:=[1, 3, 8, 18]; [n le 4 select I[n] else Self(n-1) +10*Self(n-3) -10*Self(n-4): n in [1..40]]; // G. C. Greubel, Jul 23 2023
(SageMath) [sum((1 + (j%3)^2)*10^(j//3) for j in range(n+1)) for n in range(41)] # G. C. Greubel, Jul 23 2023
CROSSREFS
Sequence in context: A051633 A172265 A258272 * A117713 A128552 A238361
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Apr 14 2006
STATUS
approved