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A273513
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a(n) is the number of arithmetic triples n<p<q (three numbers in arithmetic progression) such that p and q contain no 2's in their ternary representation.
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4
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0, 0, 1, 0, 0, 1, 1, 1, 2, 0, 0, 1, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 2, 2, 3, 0, 0, 1, 0, 0, 1, 1, 1, 2, 0, 0, 1, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 4, 3, 3, 5, 2, 2, 4, 2, 2, 5, 3, 3, 4, 0, 0, 1, 0, 0, 1
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OFFSET
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0,9
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COMMENTS
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This is a recursive sequence that gives the number of times n is rejected from A005836, if n is the smallest member of an arithmetic triple whose final two terms are contained in A005836.
This is similar to both A002487, which has a similar recurrence relation and counts hyperbinary representations of n, and A000119, which counts representations of n as a sum of distinct Fibonacci numbers.
Indices of maxima between a(n) and a(k) appear to converge to (3/4)(k-n) and (11/12)(k-n).
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LINKS
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FORMULA
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a(0)=0, a(n)=a(3n)=a(3n+1);
if a(n+1)=0, a(3n+2)=1+a(n), otherwise a(3n+2)=a(n)+a(n+1).
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MAPLE
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f:= proc(n) option remember; local m;
m:= floor(n/3);
if n mod 3 <> 2 then procname(m)
elif procname(m+1)=0 then 1 + procname(m)
else procname(m) + procname(m+1)
fi
end proc:
f(0):= 0:
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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