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A002277
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a(n) = 3*(10^n - 1)/9.
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45
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0, 3, 33, 333, 3333, 33333, 333333, 3333333, 33333333, 333333333, 3333333333, 33333333333, 333333333333, 3333333333333, 33333333333333, 333333333333333, 3333333333333333, 33333333333333333
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OFFSET
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0,2
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COMMENTS
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From Wolfdieter Lang, Feb 08 2017: (Start)
This sequence (for n >= 1) appears in n-families satisfying so-called curious cubic identities based on the Armstrong numbers 153, 370 and 371, A005188(10) - A005188(12).
153 also involves A246057(n-1) and A093143(n). See a comment in A246057 with the van Poorten et al. reference, and A281857.
370 and 371 also involve A067275(n+1). See the comment there, and A281858 and A281860. (End)
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LINKS
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Ivan Panchenko, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (11,-10).
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FORMULA
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a(n) = 3*A002275(n).
a(n) = 10*a(n-1) + 3, with a(0)=0. - Paolo P. Lava, Jan 23 2009
a(n) = A178631(n)/A002283(n). - Reinhard Zumkeller, May 31 2010
From Vincenzo Librandi, Jul 22 2010: (Start)
a(n) = a(n-1) + 3*10^(n-1) with a(0)=0;
a(n) = 11*a(n-1) - 10*a(n-2) with a(0)=0, a(1)=3. (End)
G.f.: 3*x/((1 - x)*(1 - 10*x)). - Ilya Gutkovskiy, Feb 24 2017
Sum_{n>=1} 1/a(n) = A135702. - Amiram Eldar, Nov 13 2020
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EXAMPLE
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From Wolfdieter Lang, Feb 08 2017: (Start)
Curious cubic identities (see a comment above):
1^3 + 5^3 + 3^3 = 153, 16^3 + 50^3 + 33^3 = 165033, 166^3 + 500^3 + 333^3 = 166500333, ...
3^3 + 7^3 + 0^3 = 370; 336700 = 33^3 + 67^3 + (00)^3 = 336700, 333^3 + 667^3 + (000)^3 = 333667000, ...
3^3 + 7^3 + 1^3 = 371, 33^3 + 67^3 + (01)^3 = 336701, 333^3 + 667^3 + (001)^3 = 333667001, ... (End)
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MAPLE
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A002277:=n->(10^n-1)/3: seq(A002277(n), n=0..30); # Wesley Ivan Hurt, Apr 01 2016
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MATHEMATICA
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LinearRecurrence[{11, -10}, {0, 3}, 20] (* Robert G. Wilson v, Jul 06 2013 *)
(10^Range[0, 30] - 1)/3 (* Wesley Ivan Hurt, Apr 01 2016 *)
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PROG
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(Maxima) A002277(n):=(10^n - 1)/3$
makelist(A002277(n), n, 0, 20); /* Martin Ettl, Nov 12 2012 */
(PARI) a(n)=(10^n-1)/3 \\ Charles R Greathouse IV, Sep 24 2015
(MAGMA) [(10^n - 1)/3 : n in [0..30]]; // Wesley Ivan Hurt, Apr 01 2016
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CROSSREFS
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Cf. A002275, A002276, A002278, A002279, A002280, A002281, A002282, A002283.
Cf. A075412, A135702, A178631, A178633.
Sequence in context: A097486 A121515 A221883 * A332087 A001507 A221162
Adjacent sequences: A002274 A002275 A002276 * A002278 A002279 A002280
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KEYWORD
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easy,nonn
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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