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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A008585(n+1) = length pf 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

√Čric 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 * A213861 A108458 A254281

Adjacent sequences:  A253669 A253670 A253671 * A253673 A253674 A253675

KEYWORD

nonn,tabf

AUTHOR

Eric Angelini and Reinhard Zumkeller, Jan 08 2015

STATUS

approved

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Last modified August 8 19:29 EDT 2020. Contains 336298 sequences. (Running on oeis4.)