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A134804
Remainder of triangular number A000217(n) modulo 9.
2
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
OFFSET
0,3
COMMENTS
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. - Paul Curtz, Mar 25 2009
FORMULA
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)].
MATHEMATICA
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 1, 3, 6, 1, 6, 3, 1, 0}, 105] (* Ray Chandler, Aug 26 2015 *)
CROSSREFS
Sequence in context: A307281 A089078 A355072 * A145389 A055263 A004157
KEYWORD
easy,nonn
AUTHOR
R. J. Mathar, Jan 28 2008
STATUS
approved