A253672 Another fractal t(h)ree.

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

Reinhard Zumkeller, Rows n = 0..100 of triangle, flattened

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

Cf. A008585, A062741.

Sequence in context: A207331 A134405 A091612 * A367562 A213861 A355173

Adjacent sequences: A253669 A253670 A253671 * A253673 A253674 A253675

Keyword

nonn,tabf

Author

Eric Angelini and Reinhard Zumkeller, Jan 08 2015

Status

approved