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a(n) = numerator( 3*(3+(-1)^n)/(n+1)^3 ).
4

%I #17 Sep 30 2020 14:46:02

%S 12,3,4,3,12,1,12,3,4,3,12,1,12,3,4,3,12,1,12,3,4,3,12,1,12,3,4,3,12,

%T 1,12,3,4,3,12,1,12,3,4,3,12,1,12,3,4,3,12,1,12,3,4,3,12,1,12,3,4,3,

%U 12,1,12,3,4,3,12,1,12,3,4,3,12,1,12,3,4,3,12,1

%N a(n) = numerator( 3*(3+(-1)^n)/(n+1)^3 ).

%C Denominator of 3*(3+(-1)^n)/(n+1)^3 is A129196.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).

%F G.f.: (12 + 3*x + 4*x^2 + 3*x^3 + 12*x^4 + x^5)/(1 - x^6).

%F Period 6: repeat [12, 3, 4, 3, 12, 1].

%t Table[3 (3+(-1)^n)/(n+1)^3,{n,0,80}]//Numerator (* _Harvey P. Dale_, Sep 26 2020 *)

%Y Cf. sequences listed in Comments section of A283393.

%K nonn,easy

%O 0,1

%A _Paul Barry_, Apr 02 2007