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A002277 a(n) = 3*(10^n - 1)/9. 33
0, 3, 33, 333, 3333, 33333, 333333, 3333333, 33333333, 333333333, 3333333333, 33333333333, 333333333333, 3333333333333, 33333333333333, 333333333333333, 3333333333333333, 33333333333333333 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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 involves also A246057(n-1) and A093143(n). See a comment in A246057 with the van Poorten et al. reference, and A281857.

370 and 371 involve also A067275(n+1). See the comment there, and A281858 and A281860. (End)

LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (11, -10).

FORMULA

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

EXAMPLE

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)

MAPLE

A002277:=n->(10^n-1)/3: seq(A002277(n), n=0..30); # Wesley Ivan Hurt, Apr 01 2016

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A002275, A002276, A002278, A002279, A002280, A002281, A002282, A002283.

Cf. A075412, A178631, A178633.

Sequence in context: A097486 A121515 A221883 * A001507 A221162 A231594

Adjacent sequences:  A002274 A002275 A002276 * A002278 A002279 A002280

KEYWORD

easy,nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 23 13:38 EST 2018. Contains 299581 sequences. (Running on oeis4.)