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A033127 Base 9 digits are, in order, the first n terms of the periodic sequence with initial period 1,0,1. 1
1, 9, 82, 739, 6651, 59860, 538741, 4848669, 43638022, 392742199, 3534679791, 31812118120, 286309063081, 2576781567729, 23191034109562, 208719306986059, 1878473762874531, 16906263865870780, 152156374792837021, 1369407373135533189, 12324666358219798702 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved

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Last modified June 23 22:09 EDT 2024. Contains 373661 sequences. (Running on oeis4.)