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A133292
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Period 9: repeat [1, 1, 2, 4, 7, 2, 7, 4, 2].
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3
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1, 1, 2, 4, 7, 2, 7, 4, 2, 1, 1, 2, 4, 7, 2, 7, 4, 2, 1, 1, 2, 4, 7, 2, 7, 4, 2, 1, 1, 2, 4, 7, 2, 7, 4, 2, 1, 1, 2, 4, 7, 2, 7, 4, 2, 1, 1, 2, 4, 7, 2, 7, 4, 2, 1, 1, 2, 4, 7, 2, 7, 4, 2, 1, 1, 2, 4, 7, 2, 7, 4, 2, 1, 1, 2, 4, 7, 2, 7, 4, 2, 1, 1, 2, 4, 7, 2, 7, 4, 2, 1, 1, 2, 4, 7, 2, 7, 4, 2, 1, 1, 2, 4, 7, 2
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OFFSET
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0,3
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COMMENTS
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For n>0, digital roots of centered 10-gonal numbers (A062786). - Colin Barker, Jan 30 2015
For n>0, also the digital roots of central polygonal numbers (the Lazy Caterer's sequence) A000124. - Peter M. Chema, Sep 17 2016
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1).
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FORMULA
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a(n) = (1/54)*{11*(n mod 9)+17*[(n+1) mod 9]+23*[(n+2) mod 9]-25*[(n+3) mod 9]+35*[(n+4) mod 9]-13*[(n+5) mod 9]-7*[(n+6) mod 9]-[(n+7) mod 9]+5*[(n+8) mod 9]}, with n>=0. - Paolo P. Lava, Oct 24 2007
G.f.: -(2*x^8+4*x^7+7*x^6+2*x^5+7*x^4+4*x^3+2*x^2+x+1) / ((x-1)*(x^2+x+1)*(x^6+x^3+1)). - Colin Barker, Apr 04 2015
a(n) = a(n-9). - Wesley Ivan Hurt, May 09 2022
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MATHEMATICA
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PadRight[{}, 111, {1, 1, 2, 4, 7, 2, 7, 4, 2}] (* Harvey P. Dale, Apr 29 2012 *)
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PROG
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(PARI) a(n)=[1, 1, 2, 4, 7, 2, 7, 4, 2][n%9+1] \\ Charles R Greathouse IV, Jun 02 2011
(PARI) Vec(-(2*x^8+4*x^7+7*x^6+2*x^5+7*x^4+4*x^3+2*x^2+x+1)/((x-1)*(x^2+x+1)*(x^6+x^3+1)) + O(x^100)) \\ Colin Barker, Apr 04 2015
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CROSSREFS
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Cf. A000124, A062786.
Sequence in context: A134974 A244262 A166531 * A126218 A086330 A098283
Adjacent sequences: A133289 A133290 A133291 * A133293 A133294 A133295
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KEYWORD
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nonn,easy,less
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AUTHOR
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Paul Curtz, Oct 17 2007
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STATUS
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approved
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