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A253672
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Another fractal t(h)ree.
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1
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0, 1, 2, 0, 1, 3, 4, 5, 2, 0, 1, 3, 4, 6, 7, 8, 5, 2, 0, 1, 3, 4, 6, 7, 9, 10, 11, 8, 5, 2, 0, 1, 3, 4, 6, 7, 9, 10, 12, 13, 14, 11, 8, 5, 2, 0, 1, 3, 4, 6, 7, 9, 10, 12, 13, 15, 16, 17, 14, 11, 8, 5, 2, 0, 1, 3, 4, 6, 7, 9, 10, 12, 13, 15, 16, 18, 19, 20
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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the fractal nature is illustrated by the following manipulation: remove from all rows the first two terms and also the last one, after subtracting all terms by 3, the original t(h)ree will reappear.
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LINKS
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FORMULA
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T(n,0) = 0; T(n,1)=1; T(n,2*n-1) = 2; T(n+1,k+2) = T(n,k)+3, k = 0..3*n-1.
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EXAMPLE
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. 0: | 0 1 2|
. 1: 0 1 | 3 4 5| 2
. 2: 0 1 3 4 | 6 7 8| 5 2
. 3: 0 1 3 4 6 7 | 9 10 11| 8 5 2
. 4: 0 1 3 4 6 7 9 10 |12 13 14| 11 8 5 2
. 5: 0 1 3 4 6 7 9 10 12 13 |15 16 17| 14 11 8 5 2
. 6: 0 1 3 4 6 7 9 10 12 13 15 16 |18 19 20| 17 14 11 8 5 2
. 7: 0 1 3 4 6 7 9 10 12 13 15 16 18 19 |21 22 23| 20 17 14 11 8 5 2 .
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PROG
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(Haskell)
a253672 n k = a253672_tabf !! n !! k
a253672_row n = a253672_tabf !! n
a253672_tabf = [0, 1, 2] : f [] [0, 1, 2] [] (iterate (map (+ 3)) [3..5]) where
f as bs cs (uvws:uvwss) = (as' ++ uvws ++ cs') : f as' uvws cs' uvwss
where as' = as ++ [u, v]; cs' = [w] ++ cs
[u, v, w] = bs
a253672_list = concat a253672_tabf
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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