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A309494 a(1) = a(2) = a(3) = a(5) = 1, a(4) = 2; a(n) = a(n-a(n-3)) + a(n-a(n-4)) for n > 5.

%I A309494 #33 Aug 08 2019 07:41:59
%S A309494 1,1,1,2,1,2,3,5,8,8,7,5,2,5,13,12,18,3,5,6,4,23,21,9,5,2,5,26,14,31,
%T A309494 3,5,6,4,36,34,9,5,2,5,39,14,44,3,5,6,4,49,47,9,5,2,5,52,14,57,3,5,6,
%U A309494 4,62,60,9,5,2,5,65,14,70,3,5,6,4,75,73,9,5,2,5,78,14,83,3,5,6,4,88,86,9,5,2,5,91
%N A309494 a(1) = a(2) = a(3) = a(5) = 1, a(4) = 2; a(n) = a(n-a(n-3)) + a(n-a(n-4)) for n > 5.
%C A309494 A well-defined solution sequence for recurrence a(n) = a(n-a(n-3)) + a(n-a(n-4)).
%H A309494 Robert Israel, <a href="/A309494/b309494.txt">Table of n, a(n) for n = 1..10000</a>
%H A309494 <a href="/index/Rec#order_26">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,-1).
%F A309494 For k > 1,
%F A309494   a(13*k-9) = 13*k-8,
%F A309494   a(13*k-8) = 3,
%F A309494   a(13*k-7) = 5,
%F A309494   a(13*k-6) = 6,
%F A309494   a(13*k-5) = 4,
%F A309494   a(13*k-4) = 13*k-3,
%F A309494   a(13*k-3) = 13*k-5,
%F A309494   a(13*k-2) = 9,
%F A309494   a(13*k-1) = 5,
%F A309494   a(13*k)   = 2,
%F A309494   a(13*k+1) = 5,
%F A309494   a(13*k+2) = 13*k,
%F A309494   a(13*k+3) = 14.
%F A309494 From _Colin Barker_, Aug 05 2019: (Start)
%F A309494 G.f.: x*(1 + x + x^2 + 2*x^3 + x^4 + 2*x^5 + 3*x^6 + 5*x^7 + 8*x^8 + 8*x^9 + 7*x^10 + 5*x^11 + 2*x^12 + 3*x^13 + 11*x^14 + 10*x^15 + 14*x^16 + x^17 + x^18 - 6*x^20 + 7*x^21 + 5*x^22 - 5*x^23 - 5*x^24 - 2*x^25 - 4*x^26 + x^27 - 9*x^28 - 3*x^29 - 2*x^30 - 3*x^31 - 3*x^32 + x^33 - 2*x^34 - 2*x^36 - 2*x^41) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12)^2).
%F A309494 a(n) = 2*a(n-13) - a(n-26) for n > 42.
%F A309494 (End)
%p A309494 for n from 1 to 5 do a[n]:= `if`(n=4,2,1) od:
%p A309494 for n from 6 to 100 do a[n]:= a[n-a[n-3]] + a[n-a[n-4]] od:
%p A309494 seq(a[n],n=1..100); # _Robert Israel_, Aug 07 2019
%t A309494 a[1]=a[2]=a[3]=a[5]=1; a[4]=2; a[n_] := a[n] = a[n - a[n-3]] + a[n - a[n-4]]; Array[a, 93] (* _Giovanni Resta_, Aug 07 2019 *)
%o A309494 (PARI) q=vector(100); q[1]=q[2]=q[3]=q[5]=1; q[4]=2; for(n=6, #q, q[n]=q[n-q[n-3]]+q[n-q[n-4]]); q
%o A309494 (PARI) Vec(x*(1 + x + x^2 + 2*x^3 + x^4 + 2*x^5 + 3*x^6 + 5*x^7 + 8*x^8 + 8*x^9 + 7*x^10 + 5*x^11 + 2*x^12 + 3*x^13 + 11*x^14 + 10*x^15 + 14*x^16 + x^17 + x^18 - 6*x^20 + 7*x^21 + 5*x^22 - 5*x^23 - 5*x^24 - 2*x^25 - 4*x^26 + x^27 - 9*x^28 - 3*x^29 - 2*x^30 - 3*x^31 - 3*x^32 + x^33 - 2*x^34 - 2*x^36 - 2*x^41) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12)^2) + O(x^80)) \\ _Colin Barker_, Aug 08 2019
%Y A309494 Cf. A064657, A244477, A309492.
%K A309494 nonn,easy
%O A309494 1,4
%A A309494 _Altug Alkan_, Aug 04 2019