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%I #42 Jun 22 2017 05:46:45
%S 0,1,0,4,4,4,3,12,8,4,3,24,12,4,3,40,16,4,3,60,20,4,3,84,24,4,3,112,
%T 28,4,3,144,32,4,3,180,36,4,3,220,40,4,3,264,44,4,3,312,48,4,3,364,52,
%U 4,3,420,56,4,3,480,60,4,3,544,64,4,3,612,68,4,3,684
%N An eventually quasi-quadratic sequence satisfying a Hofstadter-like recurrence.
%C a(n) is the solution to the recurrence relation a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)), with the initial conditions: a(n) = 0 if n <= 0; a(1) = 0, a(2) = 1, a(3) = 0, a(4) = 4, a(5) = 4, a(6) = 4, a(7) = 3.
%H Colin Barker, <a href="/A268368/b268368.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,3,0,0,0,-3,0,0,0,1).
%F a(2) = 1, a(3) = 0; otherwise a(4n) = 2n^2+2n, a(4n+1) = 4n, a(4n+2) = 4, a(4n+3) = 3.
%F From _Colin Barker_, Jun 22 2017: (Start)
%F G.f.: x^2*(1 + 4*x^2 + 4*x^3 + x^4 + 3*x^5 - 4*x^7 - 5*x^8 - 6*x^9 + 3*x^12 + 3*x^13) / ((1 - x)^3*(1 + x)^3*(1 + x^2)^3).
%F a(n) = 3*a(n-4) - 3*a(n-8) + a(n-12) for n>12.
%F (End)
%o (PARI) concat(0, Vec(x^2*(1 + 4*x^2 + 4*x^3 + x^4 + 3*x^5 - 4*x^7 - 5*x^8 - 6*x^9 + 3*x^12 + 3*x^13) / ((1 - x)^3*(1 + x)^3*(1 + x^2)^3) + O(x^100))) \\ _Colin Barker_, Jun 22 2017
%Y Cf. A005185, A188670, A244477, A264757, A267501.
%K nonn,easy
%O 1,4
%A _Nathan Fox_, Feb 23 2016
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