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A253672
Another fractal t(h)ree.
1
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
OFFSET
0,3
COMMENTS
A008585(n+1) = length of row n; A062741(n+1) = sum of row n;
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.
LINKS
Éric Angelini, More (and more) fractal trees - and erasures, SeqFan list, Jan 08 2015.
FORMULA
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.
EXAMPLE
. 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 .
PROG
(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
CROSSREFS
Sequence in context: A207331 A134405 A091612 * A367562 A213861 A355173
KEYWORD
nonn,tabf
AUTHOR
STATUS
approved