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)).

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

Offset: 0

Author

Peter Luschny, Nov 12 2011

Keywords

• nonn
• tabf

Examples

			                         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
		

Links

• Reinhard Zumkeller, Rows n = 0..13 of triangle, flattened

Crossrefs

Cf. A094373 (row lengths), A045623 (row sums), A011782 (edges and central terms).

Programs

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

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 *)

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