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A309967 a(1) = a(2) = 1, a(3) = 2, a(4) = 3, a(5) = 8, a(6) = 6, a(7) = a(8) = 4; a(n) = a(n-a(n-1)) + a(n-a(n-4)) for n > 8.

%I A309967 #23 Aug 26 2019 12:44:22
%S A309967 1,1,2,3,8,6,4,4,9,4,8,7,9,12,6,13,7,14,17,6,18,7,19,22,6,23,7,24,27,
%T A309967 6,28,7,29,32,6,33,7,34,37,6,38,7,39,42,6,43,7,44,47,6,48,7,49,52,6,
%U A309967 53,7,54,57,6,58,7,59,62,6,63,7,64,67,6,68,7,69,72,6,73,7,74,77,6,78,7
%N A309967 a(1) = a(2) = 1, a(3) = 2, a(4) = 3, a(5) = 8, a(6) = 6, a(7) = a(8) = 4; a(n) = a(n-a(n-1)) + a(n-a(n-4)) for n > 8.
%C A309967 A quasilinear solution sequence for Hofstadter V recurrence (a(n) = a(n-a(n-1)) + a(n-a(n-4))).
%H A309967 Colin Barker, <a href="/A309967/b309967.txt">Table of n, a(n) for n = 1..1000</a>
%H A309967 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,2,0,0,0,0,-1).
%F A309967 For k > 2:
%F A309967 a(5*k-4) = 5*k-7,
%F A309967 a(5*k-3) = 7,
%F A309967 a(5*k-2) = 5*k-6,
%F A309967 a(5*k-1) = 5*k-3,
%F A309967 a(5*k) = 6.
%F A309967 From _Colin Barker_, Aug 25 2019: (Start)
%F A309967 G.f.: x*(1 + x + 2*x^2 + 3*x^3 + 8*x^4 + 4*x^5 + 2*x^6 + 3*x^8 - 12*x^9 - 3*x^10 +  3*x^12 - 3*x^13 + 6*x^14 + 3*x^15 - 3*x^16 + 2*x^18 - 2*x^19) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)^2).
%F A309967 a(n) = 2*a(n-5) - a(n-10) for n > 20.
%F A309967 (End)
%o A309967 (PARI) q=vector(100); q[1]=q[2]=1; q[3]=2; q[4]=3; q[5]=8; q[6]=6; q[7]=q[8]=4; for(n=9, #q, q[n]=q[n-q[n-1]]+q[n-q[n-4]]); q
%o A309967 (PARI) Vec(x*(1 + x + 2*x^2 + 3*x^3 + 8*x^4 + 4*x^5 + 2*x^6 + 3*x^8 - 12*x^9 - 3*x^10 +  3*x^12 - 3*x^13 + 6*x^14 + 3*x^15 - 3*x^16 + 2*x^18 - 2*x^19) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)^2) + O(x^40)) \\ _Colin Barker_, Aug 25 2019
%Y A309967 Cf. A005185, A063882, A244477, A309567, A309636.
%K A309967 nonn,easy
%O A309967 1,3
%A A309967 _Altug Alkan_, Aug 25 2019