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A198069 Table read by rows, T(0,0) = 1 and for n>0, 0<=k<=2^(n-1) T(n,k) = gcd(k,2^(n-1)). 5
1, 1, 1, 2, 1, 2, 4, 1, 2, 1, 4, 8, 1, 2, 1, 4, 1, 2, 1, 8, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 16, 32, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 32, 64, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
For n > 0: Let S be the n-th row, S' = replace the initial term by its double, then row (n+1) = concatenation of S' and the reverse of S' without the initial term. - Reinhard Zumkeller, May 26 2013
EXAMPLE
1
1, 1
2, 1, 2
4, 1, 2, 1, 4
8, 1, 2, 1, 4, 1, 2, 1, 8
16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 16
MAPLE
# In triangular form:
seq(print(seq(gcd(k, 2^(n-1)), k=0..2^(n-1))), n=0..6);
MATHEMATICA
Join[{1}, Flatten[Table[GCD[k, 2^(n-1)], {n, 10}, {k, 0, 2^(n-1)}]]] (* Harvey P. Dale, Oct 30 2021 *)
PROG
(Haskell)
a198069 n k = a198069_tabf !! n !! k
a198069_row n = a198069_tabf !! n
a198069_tabf = [0] : iterate f [1, 1] where
f (x:xs) = ys ++ tail (reverse ys) where ys = (2 * x) : xs
-- Reinhard Zumkeller, May 26 2013
CROSSREFS
Cf. A094373 (row lengths), A045623 (row sums), A011782 (edges and central terms).
Sequence in context: A328027 A193829 A337714 * A300792 A132082 A129644
KEYWORD
nonn,tabf
AUTHOR
Peter Luschny, Nov 12 2011
STATUS
approved

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Last modified April 23 16:28 EDT 2024. Contains 371916 sequences. (Running on oeis4.)