A037559 Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 2,1,1.

2, 21, 211, 2112, 21121, 211211, 2112112, 21121121, 211211211, 2112112112, 21121121121, 211211211211, 2112112112112, 21121121121121, 211211211211211, 2112112112112112

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..990

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

Formula

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

a(n) = (633*10^n - 444 - 27*( 7*A049347(n) + 3*A049347(n-1) ))/2997. - G. C. Greubel, Oct 18 2022

Mathematica

Table[FromDigits[PadRight[{}, n, {2, 1, 1}]], {n, 20}] (* Harvey P. Dale, Jul 15 2019 *)

Prog

(PARI) Vec(x*(2+x+x^2) / ((x-1)*(10*x-1)*(1+x+x^2)) + O(x^25)) \\ Jinyuan Wang, Apr 14 2020
(Magma) I:=[2, 21, 211, 2112]; [n le 4 select I[n] else 10*Self(n-1) +Self(n-3) -10*Self(n-4): n in [1..40]]; // G. C. Greubel, Oct 18 2022
(SageMath)
def A037559(n): return (633*10^n -444 -27*(7*chebyshev_U(n, -1/2) + 3*chebyshev_U(n-1, -1/2)))/2997
[A037559(n) for n in range(1, 40)] # G. C. Greubel, Oct 18 2022

Crossrefs

Cf. A049347.

Sequence in context: A037736 A328073 A329318 * A042349 A037495 A024763

Adjacent sequences: A037556 A037557 A037558 * A037560 A037561 A037562

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved