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A021115
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Decimal expansion of 1/111.
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1
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0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9, 0, 0, 9
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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G.f.: 9*x^2/(1 - x^3).
a(n) = (9/2)*( (n-1)*n mod 3 ) = 4*(n mod 3) - 2*((n+1) mod 3) + ((n+2) mod 3), formulas suggested by Giovanni Resta.
a(n) = 3*( 1 + cos(2*(n+1)*Pi/3) + cos(4*(n+1)*Pi/3) ).
a(n) = a(n + 3) for n>2.
a(n) = A056992(n+1) - (3*(n+1)^4+3*(n+1)^6+4*(n+1)^8) mod 9. (End)
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MAPLE
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MATHEMATICA
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PROG
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(PARI) a(n) = 9*(n*(n-1)%3)/2;
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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