A033123 Base-5 digits are, in order, the first n terms of the periodic sequence with initial period 1,0,1.

1, 5, 26, 131, 655, 3276, 16381, 81905, 409526, 2047631, 10238155, 51190776, 255953881, 1279769405, 6398847026, 31994235131, 159971175655, 799855878276, 3999279391381, 19996396956905, 99981984784526, 499909923922631, 2499549619613155, 12497748098065776

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,0,1,-5).

Formula

a(n) = 5*a(n-1) + a(n-3) - 5*a(n-4).

G.f.: x*(1+x^2) / ((1-x)*(1-5*x)*(1+x+x^2)). - Colin Barker, Dec 24 2015

Mathematica

Table[FromDigits[PadRight[{}, n, {1, 0, 1}], 5], {n, 30}] (* or *) LinearRecurrence[ {5, 0, 1, -5}, {1, 5, 26, 131}, 30] (* Harvey P. Dale, Mar 25 2019 *)

Prog

(PARI) Vec(x*(1+x^2)/((1-x)*(1-5*x)*(1+x+x^2)) + O(x^30)) \\ Colin Barker, Dec 24 2015

Crossrefs

Sequence in context: A244617 A003583 A033115 * A331883 A047770 A047757

Adjacent sequences: A033120 A033121 A033122 * A033124 A033125 A033126

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved