cp's OEIS Frontend

A373234 Relative of Hofstadter Q-sequence: a(n) = max(0, n+196) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.

%I A373234 #10 May 30 2024 22:11:03
%S A373234 6,197,198,199,9,200,201,202,12,203,204,205,15,206,207,17,209,18,209,
%T A373234 211,212,22,21,403,397,9,18,412,415,205,22,226,231,209,27,36,233,402,
%U A373234 200,39,234,240,204,42,236,243,16,235,243,223,40,235,55,416,212,46,245,256,25,38,58,835,406,200,61,71,455,394,194,72,268,270,7,457,395
%N A373234 Relative of Hofstadter Q-sequence: a(n) = max(0, n+196) for n <= 0;  a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.
%C A373234 Sequences like this are more naturally considered with the first nonzero term in position 1. But this sequence would then match A000027 for its first 196 terms.
%C A373234 This sequence has exactly 223 terms (of positive index).  a(223) = 0, so an attempt to calculate a(224) would refer to itself.
%C A373234 Without the convention that a(n) = 0 for n <= -196, this sequence would have exactly 24 terms (of positive index), since computing a(25) refers to a(-378).
%C A373234 If 196 in this sequence's definition is replaced by any larger number congruent to 0 mod 7, the behavior is essentially the same, though the quasilinear part (see Formula section) lasts longer.
%H A373234 Nathan Fox, <a href="/A373234/b373234.txt">Table of n, a(n) for n = 1..223</a>
%F A373234 If the index is between 67 and 195 (inclusive), then a(7n) = 7n+2, a(7n+1) = 7n+198, a(7n+2) = 7n+200, a(7n+3) = 7, a(7n+4) = 2n+437, a(7n+5) = n+385, a(7n+6) = 194.
%Y A373234 Cf. A005185, A267501, A278055, A373235, A373236, A373237, A373238, A274058, A373239.
%K A373234 nonn,fini,full
%O A373234 1,1
%A A373234 _Nathan Fox_, May 28 2024