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A253580 A fractal tree, read by rows: for n > 1: T(n,0) = T(n-1,0)+2, T(n,2*n) = T(n-1,0)+3, and for k=1..2*n-1: T(n,k) = T(n-1,k-1). 5
0, 1, 0, 2, 3, 1, 0, 2, 4, 5, 3, 1, 0, 2, 4, 6, 7, 5, 3, 1, 0, 2, 4, 6, 8, 9, 7, 5, 3, 1, 0, 2, 4, 6, 8, 10, 11, 9, 7, 5, 3, 1, 0, 2, 4, 6, 8, 10, 12, 13, 11, 9, 7, 5, 3, 1, 0, 2, 4, 6, 8, 10, 12, 14, 15, 13, 11, 9, 7, 5, 3, 1, 0, 2, 4, 6, 8, 10, 12, 14, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

If all pairs of consecutive terms (i,i+1) (such as (0,1), (1,2), (2,3), ...) are erased, the original sequence appears; see also A253607.

T(n,n-k) + T(n,n+k) = 4*k - 1 for k = 1..n;

T(n+m,k) = T(n,k) for m > 0, k = 0 .. 2*n.

REFERENCES

V. A. Sankar Ponnapalli and V. Y. Jayasree Pappu, Design of Octagonal Fractal Array Antenna for Side Lobe Reduction with Morse-Thue Fractal Density Tapering Technique, Preprint, 2016.

LINKS

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

Éric Angelini, More fractal trees - and erasures, SeqFan list, Jan 04 2015.

EXAMPLE

.   0:                                 0

.   1:                               1 0 2

.   2:                             3 1 0 2 4

.   3:                           5 3 1 0 2 4 6

.   4:                         7 5 3 1 0 2 4 6 8

.   5:                       9 7 5 3 1 0 2 4 6 8 10

.   6:                    11 9 7 5 3 1 0 2 4 6 8 10 12

.   7:                 13 11 9 7 5 3 1 0 2 4 6 8 10 12 14

.   8:              15 13 11 9 7 5 3 1 0 2 4 6 8 10 12 14 16

.   9:           17 15 13 11 9 7 5 3 1 0 2 4 6 8 10 12 14 16 18

.  10:        19 17 15 13 11 9 7 5 3 1 0 2 4 6 8 10 12 14 16 18 20

.  11:     21 19 17 15 13 11 9 7 5 3 1 0 2 4 6 8 10 12 14 16 18 20 22

.  12:  23 21 19 17 15 13 11 9 7 5 3 1 0 2 4 6 8 10 12 14 16 18 20 22 24 .

MATHEMATICA

a[n_, k_] := 2 Abs[n-k] - Boole[k<n]; Table[a[n, k], {n, 0, 9}, {k, 0, 2 n}] // Flatten (* Jean-François Alcover, Nov 04 2016, after M. F. Hasler *)

PROG

(Haskell)

a253580 n k = a253580_tabf !! n !! k

a253580_row n = a253580_tabf !! n

a253580_tabf = [0] : [1, 0, 2] : f [1, 0, 2] where

   f xs@(x:_) = ys : f ys where ys = [x + 2] ++ xs ++ [x + 3]

a253580_list = concat a253580_tabf

(PARI) a(n, k)=abs(n-k)*2-(k<n) \\ M. F. Hasler, Jan 04 2015

CROSSREFS

Cf. A014105 (row sums), A253607 (first differences as flattened list), A253146.

Sequence in context: A133623 A065862 A189117 * A020921 A293113 A154720

Adjacent sequences:  A253577 A253578 A253579 * A253581 A253582 A253583

KEYWORD

nonn,tabf,easy,nice,look

AUTHOR

Eric Angelini and Reinhard Zumkeller, Jan 04 2015

EXTENSIONS

Typo in definition corrected by M. F. Hasler, Jan 04 2015

STATUS

approved

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Last modified April 23 07:51 EDT 2019. Contains 322381 sequences. (Running on oeis4.)