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

0,2

Links

Table of n, a(n) for n=0..90.

Example

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;
  ...

Mathematica

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 *)

Crossrefs

Product of A127243 with A127247.

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

Sequence in context: A284467 A200227 A316230 * A127251 A063251 A060208

Adjacent sequences: A127246 A127247 A127248 * A127250 A127251 A127252

Keyword

easy,nonn,tabl

Author

Paul Barry, Jan 10 2007

Extensions

More terms from Amiram Eldar, Aug 04 2023

Status

approved