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A240809
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a(n) = n for 1 <= n <= 4; thereafter a(n) = a(n - a(n-2)) + a(n - a(n-4)).
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5
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1, 2, 3, 4, 6, 6, 5, 6, 7, 8, 10, 10, 9, 10, 12, 12, 12, 12, 10, 12, 17, 16, 15, 16, 14, 16, 19, 20, 20, 18, 20, 20, 18, 22, 24, 22, 19, 24, 24, 24, 28, 24, 22, 24, 27, 32, 26, 28, 31, 28, 26, 32, 35, 32, 32, 32, 30, 32, 39, 40, 36, 34, 35, 34, 38, 40, 40, 42, 40, 38, 40, 40, 36, 44, 48, 42, 48, 44, 40, 46, 46, 46, 41, 48, 48, 48, 56, 48, 46, 48, 51, 48
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OFFSET
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1,2
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COMMENTS
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Conjectured to be infinite.
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REFERENCES
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D. R. Hofstadter, Curious patterns and non-patterns in a family of meta-Fibonacci recursions, Lecture in Doron Zeilberger's Experimental Mathematics Seminar, Rutgers University, April 10 2014.
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LINKS
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D. R. Hofstadter, Curious patterns and non-patterns in a family of meta-Fibonacci recursions, Lecture in Doron Zeilberger's Experimental Mathematics Seminar, Rutgers University, April 10 2014; Part 1, Part 2.
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MAPLE
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# Q(r, s) with initial values 1, 2, 3, 4, ...
r:=2; s:=4;
a:=proc(n) option remember; global r, s;
if n <= s then n
else
if (a(n-r) <= n) and (a(n-s) <= n) then
a(n-a(n-r))+a(n-a(n-s));
else lprint("died with n =", n); return (-1);
fi;
fi; end;
[seq(a(n), n=1..100)];
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PROG
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(Magma) I:=[1, 2, 3, 4]; [n le 4 select I[n] else Self(n-Self(n-2))+Self(n-Self(n-4)): n in [1..100]]; // Vincenzo Librandi, Apr 16 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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