A037551 Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 1,2,2.

1, 12, 122, 1221, 12212, 122122, 1221221, 12212212, 122122122, 1221221221, 12212212212, 122122122122, 1221221221221, 12212212212212, 122122122122122, 1221221221221221

Offset

1,2

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*(1+2*x+2*x^2) / ( (x-1)*(10*x-1)*(1+x+x^2) ). - R. J. Mathar, Aug 12 2013

a(1)=1, a(2)=12, a(3)=122, a(4)=1221, a(n) = 10*a(n-1) + a(n-3) - 10*a(n-4). - Harvey P. Dale, Jan 20 2015

Mathematica

With[{nn=20}, Table[FromDigits[PadRight[{}, n, {1, 2, 2}]], {n, nn}]] (* or *) LinearRecurrence[{10, 0, 1, -10}, {1, 12, 122, 1221}, 20] (* Harvey P. Dale, Jan 20 2015 *)

Prog

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

Crossrefs

Sequence in context: A231869 A038490 A329360 * A134584 A090843 A132927

Adjacent sequences: A037548 A037549 A037550 * A037552 A037553 A037554

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved