A037743 Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 2,1,3,0.

2, 21, 213, 2130, 21302, 213021, 2130213, 21302130, 213021302, 2130213021, 21302130213, 213021302130, 2130213021302, 21302130213021, 213021302130213, 2130213021302130, 21302130213021302, 213021302130213021, 2130213021302130213, 21302130213021302130

Offset

1,1

Links

Table of n, a(n) for n=1..20.

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

Formula

a(n) = 10*a(n-1) + a(n-4) - 10*a(n-5). G.f.: x*(2+x+3*x^2) / ((x-1)*(10*x-1)*(1+x)*(x^2+1)). - R. J. Mathar, Oct 05 2009

Mathematica

nn=10; With[{c=PadLeft[{}, 4nn, {2, 1, 3, 0}]}, Table[FromDigits[Take[c, n]], {n, 4nn}]] (* Harvey P. Dale, Aug 16 2011 *)

Prog

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

Crossrefs

Sequence in context: A037575 A305659 A008351 * A037638 A131698 A163068

Adjacent sequences: A037740 A037741 A037742 * A037744 A037745 A037746

Keyword

nonn,base,easy

Author

Clark Kimberling

Extensions

More terms from Harvey P. Dale, Aug 16 2011

Status

approved