A127249 -id:A127249 - cp's OEIS frontend

A127251 Inverse of number triangle A127249.

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 A127248 and A127244.
Row sums are A127252.
Cf. A127249.

T1[n_, k_] := SeriesCoefficient[(1 - ThueMorse[1 + k]*x)*x^k, {x, 0, n}]; (* A127248 *)
T2[n_, k_] := (-1)^(n-k) * Product[ThueMorse[i], {i, k+1, n}]; (* A127244 *)
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

A127250 Sequence consisting of 1,3 or 5 with 3's occurring at the odious indices given by A091855 and 5's occurring at twice these odious indices.

Original entry on oeis.org

1, 3, 5, 1, 3, 1, 1, 3, 5, 1, 1, 3, 1, 3, 5, 1, 3, 1, 1, 3, 1, 3, 5, 1, 1, 3, 5, 1, 3, 1, 1, 3, 5, 1, 1, 3, 1, 3, 5, 1, 1, 3, 5, 1, 3, 1, 1, 3, 1, 3, 5, 1, 3, 1, 1, 3, 5, 1, 1, 3, 1, 3, 5, 1, 3, 1, 1, 3, 1, 3, 5, 1, 1, 3, 5, 1, 3, 1, 1, 3, 1, 3, 5, 1, 3, 1, 1

Offset: 0

Paul Barry, Jan 10 2007

Row sums of triangle A127249.

Cf. A000069, A091855.

a[n_] := If[OddQ[DigitCount[n, 2, 1]], If[EvenQ[IntegerExponent[n, 2]], 3, 5], 1]; Array[a, 100, 0] (* Amiram Eldar, Aug 04 2023 *)

More terms from Amiram Eldar, Aug 04 2023

cp's OEIS Frontend

A127251 Inverse of number triangle A127249.

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