A037567 Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 2,2,1.

2, 22, 221, 2212, 22122, 221221, 2212212, 22122122, 221221221, 2212212212, 22122122122, 221221221221, 2212212212212, 22122122122122, 221221221221221, 2212212212212212, 22122122122122122, 221221221221221221, 2212212212212212212, 22122122122122122122, 221221221221221221221

Offset

1,1

Links

Edward Jiang, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (10,0,1,-10).

Formula

G.f.: x*(2+2*x+x^2) / ( (x-1)*(10*x-1)*(1+x+x^2) ). - R. J. Mathar, Nov 21 2011

From Robert Israel, Sep 12 2014: (Start)

a(n) = floor(221/999 * 10^n).

a(n) = 10*a(n-1) + 1 + (n^2 mod 3). (End)

Maple

seq(floor(221/999*10^n), n=1..30); # Robert Israel, Sep 12 2014

Mathematica

CoefficientList[Series[x*(2+2*x+x^2) / ((x-1)*(10*x-1)*(1+x+x^2)), {x, 0, 30}], x] (* Stefano Spezia, Nov 17 2025 *)

Prog

(PARI) a(n)=my(S=Str); for(i=0, n-1, S=concat(S, [2, 2, 1][i%3+1])); return(eval(S)) \\ Edward Jiang, Sep 11 2014

Crossrefs

Sequence in context: A239688 A350965 A336894 * A174200 A137109 A002276

Adjacent sequences: A037564 A037565 A037566 * A037568 A037569 A037570

Keyword

nonn,base

Author

Clark Kimberling

Status

approved