A037577 Base 5 digits are, in order, the first n terms of the periodic sequence with initial period 1,3.

1, 8, 41, 208, 1041, 5208, 26041, 130208, 651041, 3255208, 16276041, 81380208, 406901041, 2034505208, 10172526041, 50862630208, 254313151041, 1271565755208, 6357828776041, 31789143880208, 158945719401041, 794728597005208

Offset

1,2

Comments

This is a particular case of the generalized sequence a(n)=((A^n) - B)/(A-B). Sometimes the primes of this form are of interest, see A001348, A014224, A028491. - Ctibor O. Zizka, Apr 15 2008

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,1,-5).

Formula

a(n) = (5^n - 2)/3 for n odd ; a(n) = (5^n - 1)/3 for n even. - Ctibor O. Zizka, Apr 15 2008

a(n) = floor(5^n/3). - Gary Detlefs, Sep 06 2010

a(n) = 5*a(n-1) + a(n-2) - 5*a(n-3). - Charles R Greathouse IV, Jan 15 2011

G.f.: x*(3*x+1) / ((x-1)*(x+1)*(5*x-1)). - Colin Barker, Dec 27 2012

Example

a(1) = (5-1)/3 = 1, a(2) = (5^2-1)/3 = 8. - Philippe Deléham, Nov 15 2013

Mathematica

CoefficientList[Series[(3 x + 1)/((x - 1) (x + 1) (5 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 21 2013 *)

Crossrefs

Sequence in context: A188180 A026968 A026978 * A265149 A209822 A051737

Adjacent sequences: A037574 A037575 A037576 * A037578 A037579 A037580

Keyword

nonn,base,easy

Author

Clark Kimberling

Extensions

First formula corrected by Philippe Deléham, Nov 14 2013

Status

approved