This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A309496 #22 Sep 08 2022 08:46:21
%S A309496 1,3,6,6,2,6,4,6,10,12,6,12,10,9,16,18,6,16,18,9,22,24,6,22,24,9,28,
%T A309496 30,6,28,30,9,34,36,6,34,36,9,40,42,6,40,42,9,46,48,6,46,48,9,52,54,6,
%U A309496 52,54,9,58,60,6,58,60,9,64,66,6,64,66,9,70,72,6,70,72,9,76,78,6,76,78,9,82,84,6,82,84,9,88
%N A309496 a(1) = 1, a(2) = 3, a(3) = a(4) = a(6) = 6, a(5) = 2, a(7) = 4; a(n) = a(n-a(n-4)) + a(n-a(n-5)) for n > 7.
%C A309496 A well-defined solution sequence for recurrence a(n) = a(n-a(n-4)) + a(n-a(n-5)).
%H A309496 Colin Barker, <a href="/A309496/b309496.txt">Table of n, a(n) for n = 1..1000</a>
%H A309496 <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 A309496 For k > 2:
%F A309496 a(6*k-4) = 9,
%F A309496 a(6*k-3) = 6*k-2,
%F A309496 a(6*k-2) = 6*k,
%F A309496 a(6*k-1) = 6,
%F A309496 a(6*k) = 6*k-2,
%F A309496 a(6*k+1) = 6*k.
%F A309496 From _Colin Barker_, Aug 05 2019: (Start)
%F A309496 G.f.: x*(1 + 3*x + 6*x^2 + 5*x^3 - x^4 - 3*x^6 + x^7 - 2*x^8 + 3*x^9 + x^10 + 2*x^11 - x^13 - 3*x^16 - 2*x^17 + 2*x^18 + 2*x^20 - 2*x^21) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x + x^2)^2).
%F A309496 a(n) = a(n-3) + a(n-6) - a(n-9) for n > 22.
%F A309496 (End)
%t A309496 a[n_] := a[n] = If[n < 8, {1, 3, 6, 6, 2, 6, 4}[[n]], a[n - a[n-4]] + a[n - a[n-5]]]; Array[a, 87] (* _Giovanni Resta_, Aug 07 2019 *)
%o A309496 (PARI) q=vector(100); q[1]=1; q[2]=3; q[3]=q[4]=q[6]=6; q[5]=2; q[7]=4; for(n=8, #q, q[n] = q[n-q[n-4]]+q[n-q[n-5]]); q
%o A309496 (PARI) Vec(x*(1 + 3*x + 6*x^2 + 5*x^3 - x^4 - 3*x^6 + x^7 - 2*x^8 + 3*x^9 + x^10 + 2*x^11 - x^13 - 3*x^16 - 2*x^17 + 2*x^18 + 2*x^20 - 2*x^21) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x + x^2)^2) + O(x^80)) \\ _Colin Barker_, Aug 15 2019
%o A309496 (Magma) I:=[1,3,6,6,2,6,4];[n le 7 select I[n] else Self(n-Self(n-4))+Self(n-Self(n-5)): n in [1..90]]; // _Marius A. Burtea_, Aug 07 2019
%Y A309496 Cf. A244477, A309492, A309494.
%K A309496 nonn,easy
%O A309496 1,2
%A A309496 _Altug Alkan_, Aug 05 2019