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A127247
A Thue-Morse falling factorial triangle.
3
1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
OFFSET
0,1
COMMENTS
Central coefficients are C(1,n).
FORMULA
T(n,k) = [k<=n] * Product_{j=0..n-k-1} A010060(n-j).
EXAMPLE
Triangle begins:
1;
1, 1;
1, 1, 1;
0, 0, 0, 1;
0, 0, 0, 1, 1;
0, 0, 0, 0, 0, 1;
0, 0, 0, 0, 0, 0, 1;
0, 0, 0, 0, 0, 0, 1, 1;
0, 0, 0, 0, 0, 0, 1, 1, 1;
0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
...
MATHEMATICA
T[n_, k_] := Product[ThueMorse[i], {i, k+1, n}]; Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Amiram Eldar, Aug 04 2023 *)
CROSSREFS
Inverse is A127248.
Signed version is A127244.
Row sums are A127246.
Cf. A010060.
Sequence in context: A127507 A204441 A127244 * A144778 A143142 A174856
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Jan 10 2007
EXTENSIONS
More terms from Amiram Eldar, Aug 04 2023
STATUS
approved