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

0,2

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}]; (* 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 *)

Crossrefs

Product of A127248 and A127244.

Row sums are A127252.

Cf. A127249.

Sequence in context: A200227 A316230 A127249 * A063251 A060208 A004570

Adjacent sequences: A127248 A127249 A127250 * A127252 A127253 A127254

Keyword

sign,tabl

Author

Paul Barry, Jan 10 2007

Extensions

More terms from Amiram Eldar, Aug 04 2023

Status

approved