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A304583
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Period 18: repeat 1,8,3,6,5,4,7,2,9,0,9,2,7,4,5,6,3,8.
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2
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1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 9, 2, 7, 4, 5, 6, 3, 8, 1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 9, 2, 7, 4, 5, 6, 3, 8, 1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 9, 2, 7, 4, 5, 6, 3, 8, 1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 9, 2, 7, 4, 5, 6, 3, 8, 1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 9, 2, 7, 4
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OFFSET
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1,2
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COMMENTS
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Repeating sequences of alternating odd and even single digits that in pairs sum to 9 or 11. Note that 183654729092745638 = 2020202020020202018 / 11.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (-1,0,0,0,0,0,0,0,1,1).
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FORMULA
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G.f.: x*(1 + 9*x + 11*x^2 + 9*x^3 + 11*x^4 + 9*x^5 + 11*x^6 + 9*x^7 + 11*x^8 + 8*x^9) / ((1 - x)*(1 + x)*(1 + x + x^2)*(1 + x^3 + x^6)).
a(n) = -a(n-1) + a(n-9) + a(n-10) for n > 10.
(End)
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MATHEMATICA
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PadRight[{}, 120, {1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 9, 2, 7, 4, 5, 6, 3, 8}] (* Harvey P. Dale, Feb 10 2024 *)
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PROG
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(PARI) Vec(x*(1 + 9*x + 11*x^2 + 9*x^3 + 11*x^4 + 9*x^5 + 11*x^6 + 9*x^7 + 11*x^8 + 8*x^9) / ((1 - x)*(1 + x)*(1 + x + x^2)*(1 + x^3 + x^6)) + O(x^50)) \\ Colin Barker, May 28 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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