A037617 Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 1,3,2.

1, 13, 132, 1321, 13213, 132132, 1321321, 13213213, 132132132, 1321321321, 13213213213, 132132132132, 1321321321321, 13213213213213, 132132132132132, 1321321321321321, 13213213213213213, 132132132132132132, 1321321321321321321, 13213213213213213213, 132132132132132132132

Offset

1,2

Links

Table of n, a(n) for n=1..21.

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

Formula

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

a(n) ~ (44/333)*10^n = (44/333)*A011557(n). - Stefano Spezia, Oct 15 2023

Mathematica

Table[FromDigits[PadRight[{}, n, {1, 3, 2}]], {n, 20}] (* Harvey P. Dale, Mar 29 2015 *)

Prog

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -10, 1, 0, 10]^(n-1)*[1; 13; 132; 1321])[1, 1] \\ Charles R Greathouse IV, May 16 2026

Crossrefs

Cf. A011557.

Sequence in context: A295349 A161498 A037715 * A295603 A199144 A198664

Adjacent sequences: A037614 A037615 A037616 * A037618 A037619 A037620

Keyword

nonn,base,easy

Author

Clark Kimberling

Extensions

a(17)-a(21) from Stefano Spezia, Oct 15 2023

Status

approved