A283904 - OEIS

%I #8 Mar 18 2024 12:12:15

%S 1,1,1,2,2,1,3,3,1,4,4,2,2,7,2,2,6,3,3,11,2,3,12,2,2,14,2,2,14,3,2,14,

%T 4,14,15,1,15,18,1,18,20,1,20,22,1,22,23,1,23,25,1,25,26,1,26,28,1,28,

%U 29,1,29,31,1,31,32,1,32,34,1,34,35,1,35,37,1

%N Relative of Hofstadter Q-sequence: a(1) = 1, a(2) = 1; thereafter a(n) = a(n-2a(n-1)) + a(n-3a(n-2)).

%C This sequence is eventually quasilinear with period 6. Each component sequence has slope 0 or 1/2.

%H Nathan Fox, <a href="/A283904/b283904.txt">Table of n, a(n) for n = 1..10000</a>

%H <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 If the index is at least 41:

%F a(6n) = 1

%F a(6n+1) = 3n-1

%F a(6n+2) = 3n+1

%F a(6n+3) = 1

%F a(6n+4) = 3n+1

%F a(6n+5) = 3n+2.

%F G.f.: (-x^48-x^46-x^45-x^43+x^42+3*x^41+x^40-9*x^39-x^38+3*x^37+x^36-4*x^35+x^34+12*x^33+x^32-2*x^31+x^30+x^29-x^28+x^26-3*x^25-2*x^24-x^23+2*x^22-x^20+2*x^19+3*x^18-2*x^16-x^15+2*x^13-3*x^12+x^11-x^8+x^4+x^3+x^2+x+1) / ((1+x)*(1-x+x^2)*(-1+x)^2*(1+x+x^2)^2).

%F a(n) = a(n-3) + a(n-6) - a(n-9) for n > 49.

%p A283904:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 1: elif n = 2 then 1: else A283904(n-2*A283904(n-1)) + A283904(n-3*A283904(n-2)): fi: end:

%Y Cf. A005185, A188670, A244477.

%K nonn

%O 1,4

%A _Nathan Fox_, Mar 19 2017