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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
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: A368495 A189117 A365196 * A020921 A293113 A366528
KEYWORD
nonn,tabf,easy,nice,look
AUTHOR
EXTENSIONS
Typo in definition corrected by M. F. Hasler, Jan 04 2015
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)