A033127 Base 9 digits are, in order, the first n terms of the periodic sequence with initial period 1,0,1.

1, 9, 82, 739, 6651, 59860, 538741, 4848669, 43638022, 392742199, 3534679791, 31812118120, 286309063081, 2576781567729, 23191034109562, 208719306986059, 1878473762874531, 16906263865870780, 152156374792837021, 1369407373135533189, 12324666358219798702

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (9,0,1,-9).

Formula

a(n) = 9*a(n-1) + a(n-3) - 9*a(n-4).

G.f.: x*(x^2+1) / ((x-1)*(9*x-1)*(x^2+x+1)). - Colin Barker, Apr 30 2014

E.g.f.: exp(-x/2)*(123*exp(19*x/2) - 91*exp(3*x/2) - 32*cos(sqrt(3)*x/2) + 40*sqrt(3)*sin(sqrt(3)*x/2))/1092. - Stefano Spezia, Apr 25 2023

a(n) = floor((41/364)*9^n). - Kevin Ryde, Apr 26 2023

Mathematica

Module[{nn=20, c}, c=PadRight[{}, nn, {1, 0, 1}]; Table[FromDigits[Take[c, n], 9], {n, nn}]] (* or *) LinearRecurrence[{9, 0, 1, -9}, {1, 9, 82, 739}, 20] (* Harvey P. Dale, Jan 03 2014 *)

Prog

(PARI) Vec(x*(x^2+1)/((x-1)*(9*x-1)*(x^2+x+1)) + O(x^100)) \\ Colin Barker, Apr 30 2014
(PARI) a(n) = 41*9^n \ 364; \\ Kevin Ryde, Apr 26 2023

Crossrefs

Sequence in context: A263817 A288789 A033119 * A361715 A099371 A334611

Adjacent sequences: A033124 A033125 A033126 * A033128 A033129 A033130

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved