A117727 Partial sums of A051109.

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,10,-10).

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

Cf. A051109, A117717.

Sequence in context: A051633 A172265 A258272 * A117713 A128552 A238361

Adjacent sequences: A117724 A117725 A117726 * A117728 A117729 A117730

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 14 2006

Status

approved