A127251 -id:A127251 - cp's OEIS frontend

A127249 A product of Thue-Morse related triangles.

1, 2, 1, 2, 2, 1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 2, 2, 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, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 0

Paul Barry, Jan 10 2007

			Triangle begins:
  1;
  2, 1;
  2, 2, 1;
  0, 0, 0, 1;
  0, 0, 0, 2, 1;
  0, 0, 0, 0, 0, 1;
  0, 0, 0, 0, 0, 0, 1;
  0, 0, 0, 0, 0, 0, 2, 1;
  0, 0, 0, 0, 0, 0, 2, 2, 1;
  0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
  ...

Product of A127243 with A127247.

Inverse A127251 is given by (-1)^(n+k)T(n,k).

T1[n_, k_] := SeriesCoefficient[(1 + ThueMorse[1 + k]*x)*x^k, {x, 0, n}]; (* A127243 *)
T2[n_, k_] := Product[ThueMorse[i], {i, k + 1, n}]; (* A127247 *)
T[n_, k_] := Sum[T2[n, j]*T1[j, k], {j, 0, n}];
Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Amiram Eldar, Aug 04 2023 *)

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

A127249 A product of Thue-Morse related triangles.

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