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A304583
Period 18: repeat 1,8,3,6,5,4,7,2,9,0,9,2,7,4,5,6,3,8.
2
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
OFFSET
1,2
COMMENTS
Repeating sequences of alternating odd and even single digits that in pairs sum to 9 or 11. Note that 183654729092745638 = 2020202020020202018 / 11.
FORMULA
From Colin Barker, May 28 2018: (Start)
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)
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Halfdan Skjerning, May 15 2018
STATUS
approved