A127245 -id:A127245 - cp's OEIS frontend

A127244 A Thue-Morse signed falling factorial triangle.

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

Paul Barry, Jan 10 2007

			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;
  ...

Inverse of A127243.
Row sums are A127245.
Cf. A010060.

T[n_, k_] := (-1)^(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 *)

T(n,k) = (-1)^(n-k) * Product_{j=0..n-k-1} A010060(n-j) * [k<=n].

More terms from Amiram Eldar, Aug 04 2023

A127252 Sequence composed of 1 and -1 with the -1's occurring at odious indexed positions given by A091855.

Original entry on oeis.org

1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1

Offset: 0

Paul Barry, Jan 10 2007

Row sums of A127251.
Partial sums are A127255.
Cf. A000069, A091855, A127245.

a[n_] := If[EvenQ[IntegerExponent[n, 2]] && OddQ[DigitCount[n, 2, 1]], -1, 1]; Array[a, 100, 0] (* Amiram Eldar, Aug 04 2023 *)

More terms from Amiram Eldar, Aug 04 2023

cp's OEIS Frontend

A127244 A Thue-Morse signed falling factorial triangle.

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