login
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

%I #14 Oct 30 2021 17:43:48

%S 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,

%T 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,

%U 2,1,32,64,1,2,1,4,1,2,1,8,1,2,1,4,1,2

%N 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)).

%H Reinhard Zumkeller, <a href="/A198069/b198069.txt">Rows n = 0..13 of triangle, flattened</a>

%F 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

%e 1

%e 1, 1

%e 2, 1, 2

%e 4, 1, 2, 1, 4

%e 8, 1, 2, 1, 4, 1, 2, 1, 8

%e 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 16

%p # In triangular form:

%p seq(print(seq(gcd(k,2^(n-1)),k=0..2^(n-1))),n=0..6);

%t Join[{1},Flatten[Table[GCD[k,2^(n-1)],{n,10},{k,0,2^(n-1)}]]] (* _Harvey P. Dale_, Oct 30 2021 *)

%o (Haskell)

%o a198069 n k = a198069_tabf !! n !! k

%o a198069_row n = a198069_tabf !! n

%o a198069_tabf = [0] : iterate f [1, 1] where

%o f (x:xs) = ys ++ tail (reverse ys) where ys = (2 * x) : xs

%o -- _Reinhard Zumkeller_, May 26 2013

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

%K nonn,tabf

%O 0,4

%A _Peter Luschny_, Nov 12 2011