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A304490 a(1) = a(2) = a(3) = 1, a(4) = 5, a(5) = 6, a(6) = 4; a(n) = a(n-a(n-2)) + a(n-a(n-4)) for n > 6.

%I A304490 #18 Mar 18 2024 12:19:42
%S A304490 1,1,1,5,6,4,5,6,6,9,10,5,6,12,12,15,16,5,6,18,18,21,22,5,6,24,24,27,
%T A304490 28,5,6,30,30,33,34,5,6,36,36,39,40,5,6,42,42,45,46,5,6,48,48,51,52,5,
%U A304490 6,54,54,57,58,5,6,60,60,63,64,5,6,66,66,69,70,5,6,72,72,75,76,5,6,78,78,81,82,5,6
%N A304490 a(1) = a(2) = a(3) = 1, a(4) = 5, a(5) = 6, a(6) = 4; a(n) = a(n-a(n-2)) + a(n-a(n-4)) for n > 6.
%C A304490 A quasi-periodic solution to the recurrence a(n) = a(n-a(n-2)) + a(n-a(n-4)). Although A087777 and A240809 are highly chaotic, this sequence is completely predictable thanks to its initial conditions.
%H A304490 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (2, -3, 4, -5, 6, -5, 4, -3, 2, -1).
%F A304490 a(6*k) = 5, a(6*k+1) = 6, a(6*k+2) = a(6*k+3) = 6*k, a(6*k+4) = 6*k+3, a(6*k+5) = 6*k+4 for k > 1.
%F A304490 Conjectures from _Colin Barker_, May 14 2018: (Start)
%F A304490 G.f.: x*(1 - x + 2*x^2 + 2*x^3 + 2*x^5 - x^6 + 4*x^7 - 3*x^8 + x^9 - x^10 - 2*x^11 + 2*x^12 - x^13 + x^14 + x^15 - x^16) / ((1 - x)^2*(1 - x + x^2)^2*(1 + x + x^2)^2).
%F A304490 a(n) = 2*a(n-1) - 3*a(n-2) + 4*a(n-3) - 5*a(n-4) + 6*a(n-5) - 5*a(n-6) + 4*a(n-7) - 3*a(n-8) + 2*a(n-9) - a(n-10) for n>17.
%F A304490 (End)
%o A304490 (PARI) q=vector(85); q[1]=1;q[2]=1;q[3]=1;q[4]=5;q[5]=6;q[6]=4; for(n=7, #q, q[n] = q[n-q[n-2]]+q[n-q[n-4]]); q
%Y A304490 Cf. A087777, A240809, A244477, A296518, A296786.
%K A304490 nonn,easy
%O A304490 1,4
%A A304490 _Altug Alkan_, May 13 2018