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A134804
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Remainder of triangular number A000217(n) modulo 9.
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0
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0, 1, 3, 6, 1, 6, 3, 1, 0, 0, 1, 3, 6, 1, 6, 3, 1, 0, 0, 1, 3, 6, 1, 6, 3, 1, 0, 0, 1, 3, 6, 1, 6, 3, 1, 0, 0, 1, 3, 6, 1, 6, 3, 1, 0, 0, 1, 3, 6, 1, 6, 3, 1, 0, 0, 1, 3, 6, 1, 6, 3, 1, 0, 0, 1, 3, 6, 1, 6, 3, 1, 0, 0, 1, 3, 6, 1, 6, 3, 1, 0, 0, 1, 3, 6, 1, 6, 3, 1, 0, 0, 1, 3, 6, 1, 6, 3, 1, 0, 0, 1, 3, 6, 1, 6
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OFFSET
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0,3
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COMMENTS
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Periodic with period 9 since A000217(n+9) = A000217(n)+9(n+5) .
From Jacobsthal numbers A001045, A156060=0,1,1,3,5,2,3,7,4,0,8,=b(n). a(n)=A156060(n)*A156060(n+1) mod 9. Same transform (a(n)*a(n+1) mod 9 or b(n)*b(n+1) mod 9) in A157742,A158012,A158068,A158090 [From Paul Curtz, Mar 25 2009]
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LINKS
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Table of n, a(n) for n=0..104.
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FORMULA
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a(n) = A010878(A000217(n)) = A010878(A055263(n)) = a(n-9). O.g.f.: (-2x+2)/[3(x^2+x+1)]+(-3+3x^5)/(x^6+x^3+1)-7/[3(x-1)] .
a(n)=(1/108)*{7*(n mod 9)+19*[(n+1) mod 9]+31*[(n+2) mod 9]+43*[(n+3) mod 9]-53*[(n+4) mod 9]+67*[(n+5) mod 9]-29*[(n+6) mod 9]-17*[(n+7) mod 9]-5*[(n+8) mod 9]}, with n>=0 - Paolo P. Lava, Jan 30 2008
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CROSSREFS
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Sequence in context: A175032 A078768 A089078 * A145389 A055263 A004157
Adjacent sequences: A134801 A134802 A134803 * A134805 A134806 A134807
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KEYWORD
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easy,nonn
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AUTHOR
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R. J. Mathar, Jan 28 2008
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STATUS
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approved
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