A037638 Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 2,1,3.

2, 21, 213, 2132, 21321, 213213, 2132132, 21321321, 213213213, 2132132132, 21321321321, 213213213213, 2132132132132, 21321321321321, 213213213213213, 2132132132132132

Offset

1,1

Links

Table of n, a(n) for n=1..16.

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

Formula

G.f.: x*(2+x+3*x^2) / ( (x-1)*(10*x-1)*(1+x+x^2) ). - R. J. Mathar, Nov 21 2011

Mathematica

Table[FromDigits[PadRight[{}, n, {2, 1, 3}]], {n, 20}] (* or *) LinearRecurrence[{10, 0, 1, -10}, {2, 21, 213, 2132}, 20] (* Harvey P. Dale, Jun 23 2016 *)

Prog

(PARI) Vec(x*(2+x+3*x^2)/((x-1)*(10*x-1)*(1+x+x^2)) + O(x^25)) \\ Jinyuan Wang, Apr 14 2020

Crossrefs

Sequence in context: A305659 A008351 A037743 * A131698 A163068 A109684

Adjacent sequences: A037635 A037636 A037637 * A037639 A037640 A037641

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved