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A246999
a(n) is the binary word s21s211s2 where s is a string of n 1's.
1
212112, 121121112, 112111211112, 111211112111112, 111121111121111112, 111112111111211111112, 111111211111112111111112, 111111121111111121111111112, 111111112111111111211111111112, 111111111211111111112111111111112, 111111111121111111111121111111111112
OFFSET
0,1
COMMENTS
The word a(n) is called the n-th Biggles word. - Jamie Simpson, Oct 04 2015
LINKS
Jamie Simpson, Palindromes in circular words, Theoretical Computer Science, Volume 550, 18 September 2014, Pages 66-78; DOI: 10.1016/j.tcs.2014.07.012. See Lemma 6.
Index entries for linear recurrences with constant coefficients, signature (1111, -112110, 1111000, -1000000).
FORMULA
From Robert Israel, Sep 16 2014: (Start)
a(n) = 8/9+1000*10^n+100000*100^n+(1000000/9)*1000^n.
G.f.: 24*(8838-4772305*x+55230500*x^2-50500000*x^3)/((1-x)*(1-100*x)*(1-1000*x)*(1-10*x)). (End)
MAPLE
seq(8/9+1000*10^n+100000*100^n+(1000000/9)*1000^n, n=0..20); # Robert Israel, Sep 16 2014
MATHEMATICA
CoefficientList[Series[24 (8838 - 4772305 x + 55230500 x^2 - 50500000 x^3)/(1000000 x^4 - 1111000 x^3 + 112110 x^2 - 1111 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 12 2015 *)
Table[FromDigits[Flatten[Join[PadRight[{}, n, 1], {2, 1}, PadRight[{}, n, 1], {2, 1, 1}, PadRight[{}, n, 1], {2}]]], {n, 0, 10}] (* or *) LinearRecurrence[ {1111, -112110, 1111000, -1000000}, {212112, 121121112, 112111211112, 111211112111112}, 20] (* Harvey P. Dale, Apr 20 2018 *)
PROG
(Haskell)
a246999 n = read $ s ++ "21" ++ s ++ "211" ++ s ++ "2" :: Integer
where s = replicate n '1'
-- Reinhard Zumkeller, Sep 16 2014
(Magma) [8/9+1000*10^n+100000*100^n+(1000000/9)*1000^n: n in [0..10]]; // Vincenzo Librandi, Oct 12 2015
CROSSREFS
Sequence in context: A252880 A158993 A231418 * A186694 A143641 A184383
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Sep 15 2014
STATUS
approved