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A037582 Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 1,3. 0
1, 13, 131, 1313, 13131, 131313, 1313131, 13131313, 131313131, 1313131313, 13131313131, 131313131313, 1313131313131, 13131313131313, 131313131313131, 1313131313131313, 13131313131313131, 131313131313131313, 1313131313131313131, 13131313131313131313 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

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

FORMULA

a(n) = 10*a(n-1) + 2 + (-1)^n, with a(0)=0. Closed form: a(n) = -(2/9) + (1/11)*(-1)^n + (13/99)*10^n, with n>=1. - Paolo P. Lava, Jul 30 2009

G.f.: x*(1+3*x) / ( (x-1)*(10*x-1)*(1+x) ). - R. J. Mathar, Aug 12 2013

MATHEMATICA

Table[FromDigits[PadRight[{}, n, {1, 3}]], {n, 20}] (* Harvey P. Dale, Feb 11 2015 *)

PROG

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

CROSSREFS

Sequence in context: A037708 A142740 A248919 * A065539 A048554 A293580

Adjacent sequences:  A037579 A037580 A037581 * A037583 A037584 A037585

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Harvey P. Dale, Feb 11 2015

STATUS

approved

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Last modified September 28 02:29 EDT 2020. Contains 337392 sequences. (Running on oeis4.)