A246999 a(n) is the binary word s21s211s2 where s is a string of n 1's.

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

Reinhard Zumkeller, Table of n, a(n) for n = 0..333

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

Adjacent sequences: A246996 A246997 A246998 * A247000 A247001 A247002

Keyword

nonn,base

Author

N. J. A. Sloane, Sep 15 2014

Status

approved