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%I #16 Dec 12 2023 08:44:46
%S 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,
%T 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,
%U 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
%N Remainder of triangular number A000217(n) modulo 9.
%C Periodic with period 9 since A000217(n+9) = A000217(n)+9(n+5) .
%C 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
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 1).
%F a(n) = A010878(A000217(n)) = A010878(A055263(n)) = a(n-9).
%F O.g.f.: (-2x+2)/[3(x^2+x+1)]+(-3+3x^5)/(x^6+x^3+1)-7/[3(x-1)].
%t 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 *)
%K easy,nonn
%O 0,3
%A _R. J. Mathar_, Jan 28 2008
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