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).

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

Offset: 0

Author

Eric Angelini and Reinhard Zumkeller, Jan 04 2015

Keywords

• nonn
• tabf
• easy
• nice
• look

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.

Examples

			.   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 .
		

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.

Crossrefs

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

Programs

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

Mathematica

a[n_, k_] := 2 Abs[n-k] - Boole[kJean-François Alcover, Nov 04 2016, after M. F. Hasler *)

PARI

a(n,k)=abs(n-k)*2-(kM. F. Hasler, Jan 04 2015

Extensions

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