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A306764 a(n) is a sequence of period 12: repeat [1, 1, 6, 2, 1, 3, 2, 2, 3, 1, 2, 6].

%I A306764 #26 Dec 16 2021 18:46:30
%S A306764 1,1,6,2,1,3,2,2,3,1,2,6,1,1,6,2,1,3,2,2,3,1,2,6,1,1,6,2,1,3,2,2,3,1,
%T A306764 2,6,1,1,6,2,1,3,2,2,3,1,2,6,1,1,6,2,1,3,2,2,3,1,2,6,1,1,6,2,1,3,2,2,
%U A306764 3,1,2,6
%N A306764 a(n) is a sequence of period 12: repeat [1, 1, 6, 2, 1, 3, 2, 2, 3, 1, 2, 6].
%C A306764 a(1) to a(12) is a palindrome.
%C A306764 A089145(n) = A089128(n+3).
%C A306764 A089128(n) = A089145(n+3).
%C A306764 a(1) + a(2) + a(3) + a(4) = a(5) + a(6) + a(7) + a(8) = a(9) + a(10) + a(11) + a(12) = 10.
%H A306764 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,0,0,-1,0,0,1).
%F A306764 a(n) = 2*A064038(n+3)/A306368(n).
%F A306764 a(n) = interleave A089128(n-1), A089128(n+1).
%F A306764 a(n) = interleave A089145(n+2), A089145(n-2).
%F A306764 From _Colin Barker_, Dec 09 2019: (Start)
%F A306764 G.f.: (1 + x + 6*x^2 + x^3 - 3*x^5 + x^6 + 2*x^7 + 6*x^8) / ((1 - x)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)).
%F A306764 a(n) = a(n-3) - a(n-6) + a(n-9) for n>8.
%F A306764 (End)
%e A306764 a(0) =  6/6  = 1;
%e A306764 a(1) = 10/10 = 1;
%e A306764 a(2) = 30/5  = 6;
%e A306764 a(3) = 42/21 = 2.
%t A306764 PadRight[{},120,{1,1,6,2,1,3,2,2,3,1,2,6}] (* or *) LinearRecurrence[ {0,0,1,0,0,-1,0,0,1},{1,1,6,2,1,3,2,2,3},120] (* _Harvey P. Dale_, Dec 16 2021 *)
%o A306764 (PARI) Vec((1 + x + 6*x^2 + x^3 - 3*x^5 + x^6 + 2*x^7 + 6*x^8) / ((1 - x)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)) + O(x^80)) \\ _Colin Barker_, Dec 11 2019
%Y A306764 Cf. A064038, A089128 and A089145 (shifted bisections), A306368, A010692.
%K A306764 nonn,easy
%O A306764 0,3
%A A306764 _Paul Curtz_, Mar 08 2019