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%I #18 Mar 27 2022 13:38:20
%S 1,1,1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,9,1,10,1,11,1,12,1,1,1,2,1,3,1,4,1,
%T 5,1,6,1,7,1,8,1,9,1,10,1,11,1,12,1,1,1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,9,
%U 1,10,1,11,1,12
%N Chimes made by clock striking the hour and half-hour.
%C Periodic sequence with period 24. - _Michel Marcus_, Jul 17 2013
%H <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).
%F From _Hieronymus Fischer_, Sep 25 2007: (Start)
%F G.f.: 1/(1-x^2)+x(12x^26-13x^24+1)/((1-x^24)(1-x^2)^2).
%F G.f.: (1+x-x^2-x^24-13x^25+x^26+12x^27)/((1-x^24)(1-x^2)^2).
%F a(n) = 1 + ((n-1)*(1-(-1)^n)/4) mod 12.
%F a(n) = 1 + ((n-1)*(n mod 2)/2) mod 12. (End)
%t CoefficientList[Series[(1+x-x^2-x^24-13x^25+x^26+12x^27)/((1-x^24)(1-x^2)^2),{x,0,71}],x] (* _Stefano Spezia_, Mar 27 2022 *)
%o (PARI) a(n)= 1 + ((n-1)*(1-(-1)^n)/4) % 12 \\ _Michel Marcus_, Jul 17 2013
%Y Cf. A010881, A057979.
%K nonn,easy
%O 0,4
%A Jan Wolitzky
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