A037577 - OEIS

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

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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 *)