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%I #25 Sep 08 2022 08:46:21
%S 1,1,3,5,2,4,3,9,6,4,3,13,10,4,3,17,14,4,3,21,18,4,3,25,22,4,3,29,26,
%T 4,3,33,30,4,3,37,34,4,3,41,38,4,3,45,42,4,3,49,46,4,3,53,50,4,3,57,
%U 54,4,3,61,58,4,3,65,62,4,3,69,66,4,3,73,70,4,3,77,74,4,3,81,78,4,3,85,82,4,3
%N a(1) = a(2) = 1, a(3) = 3, a(4) = 5, a(5) = 2; a(n) = a(n-a(n-2)) + a(n-a(n-3)) for n > 5.
%C A well-defined solution sequence for recurrence a(n) = a(n-a(n-2)) + a(n-a(n-3)).
%H Colin Barker, <a href="/A309492/b309492.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1,1,-1,1,-1).
%F For k > 2:
%F a(4*k) = 4*k+1,
%F a(4*k+1) = 4*k-2,
%F a(4*k+2) = 4,
%F a(4*k+3) = 3.
%F From _Colin Barker_, Aug 04 2019: (Start)
%F G.f.: x*(1 + 3*x^2 + 2*x^3 - 2*x^4 + 4*x^5 - 7*x^6 + 6*x^7 - 3*x^8) / ((1 - x)^2*(1 + x)*(1 + x^2)^2).
%F a(n) = a(n-1) - a(n-2) + a(n-3) + a(n-4) - a(n-5) + a(n-6) - a(n-7) for n > 9.
%F (End)
%t a[n_] := a[n] = If[n < 6, {1, 1, 3, 5, 2}[[n]], a[n - a[n-2]] + a[n - a[n-3]]]; Array[a, 87] (* _Giovanni Resta_, Aug 07 2019 *)
%o (PARI) q=vector(100); q[1]=1;q[2]=1;q[3]=3;q[4]=5;q[5]=2; for(n=6, #q, q[n]=q[n-q[n-2]]+q[n-q[n-3]]); q
%o (PARI) Vec(x*(1 + 3*x^2 + 2*x^3 - 2*x^4 + 4*x^5 - 7*x^6 + 6*x^7 - 3*x^8) / ((1 - x)^2*(1 + x)*(1 + x^2)^2) + O(x^40)) \\ _Colin Barker_, Aug 15 2019
%o (Magma) I:=[1,1,3,5,2];[n le 5 select I[n] else Self(n-Self(n-2))+Self(n-Self(n-3)): n in [1..90]]; // _Marius A. Burtea_, Aug 07 2019
%Y Cf. A063892, A244477.
%K nonn,easy
%O 1,3
%A _Altug Alkan_, Aug 04 2019
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