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A053422 n times (n 1's): a(n) = n*(10^n - 1)/9. 10
0, 1, 22, 333, 4444, 55555, 666666, 7777777, 88888888, 999999999, 11111111110, 122222222221, 1333333333332, 14444444444443, 155555555555554, 1666666666666665, 17777777777777776, 188888888888888887, 1999999999999999998, 21111111111111111109, 222222222222222222220, 2333333333333333333331 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

R_a(n) is the least repunit divisible by the square of R_n = (10^n - 1)/9. - Lekraj Beedassy, Jun 07 2006

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..995

Index entries for linear recurrences with constant coefficients, signature (22,-141,220,-100).

FORMULA

a(n) = n*A002275(n) = a(n-1)*10n/(n-1) + n.

O.g.f.: x*(1-10*x^2)/((1-x)^2*(1-10*x)^2). - R. J. Mathar, Jan 21 2008

MATHEMATICA

LinearRecurrence[{22, -141, 220, -100}, {0, 1, 22, 333}, 50] (* G. C. Greubel, May 25 2018 *)

PROG

(Sage) [gaussian_binomial(n, 1, 10)*n for n in range(0, 22)] # Zerinvary Lajos, May 29 2009

(PARI) x='x+O('x^30); concat([0], Vec(x*(1-10*x^2)/((1-x)^2*(1-10*x)^2))) \\ G. C. Greubel, May 25 2018

(MAGMA) I:=[0, 1, 22, 333]; [n le 4 select I[n] else 22*Self(n-1) - 141*Self(n-2) +220*Self(n-3) -100*Self(n-4): n in [1..30]]; // G. C. Greubel, May 25 2018

CROSSREFS

Cf. A000461, A048376.

Sequence in context: A025936 A158849 A048376 * A000461 A216730 A048795

Adjacent sequences:  A053419 A053420 A053421 * A053423 A053424 A053425

KEYWORD

base,easy,nonn

AUTHOR

Henry Bottomley, Mar 07 2000

EXTENSIONS

Corrected by Jason Earls, Sep 02 2006

STATUS

approved

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Last modified April 13 21:24 EDT 2021. Contains 342941 sequences. (Running on oeis4.)