A134804 Remainder of triangular number A000217(n) modulo 9.

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

Author

R. J. Mathar, Jan 28 2008

Keywords

• easy
• nonn

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

Links

• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 1).

Programs

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 *)

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)].