A144027 Eigentriangle by rows, T(n,k) = A010060(n-k+1)*A144026(k-1), 1 <= k <= n.

1, 1, 1, 0, 1, 2, 1, 0, 2, 3, 0, 1, 0, 3, 6, 0, 0, 2, 0, 6, 10, 1, 0, 0, 3, 0, 10, 18, 1, 1, 0, 0, 6, 0, 18, 32, 0, 1, 2, 0, 0, 10, 0, 32, 58, 0, 0, 2, 3, 0, 0, 18, 0, 58, 103, 1, 0, 0, 3, 6, 0, 0, 32, 0, 103, 184, 0, 1, 0, 0, 6, 10, 0, 0, 58, 0, 184, 329, 1, 0, 2, 0, 0, 10, 18, 0, 0, 103, 329, 588

Offset

1,6

Comments

Left column = the Thue-Morse sequence A010060 starting with offset 1.

Right border = A144026: (1, 1, 2, 3, 6, 10, 18, ...).

Row sums = A144026: (1, 2, 3, 6, 10, 18, ...).

Sum of n-th row terms = rightmost term of next row.

Links

Table of n, a(n) for n=1..90.

Formula

Eigentriangle by rows, T(n,k) = A010060(n-k+1)*A144026(k-1), 1 <= k <= n.

The triangle is generated from the Thue-Morse sequence A010060 using offset 1:

(1, 1, 0, 1, 0, 0, 1, ...). A144026 is (1, 1, 2, 3, 6, 10, 18, ...).

Example

First few rows of the triangle:
  1;
  1, 1;
  0, 1, 2;
  1, 0, 2, 3;
  0, 1, 0, 3, 6;
  0, 0, 2, 0, 6, 10;
  1, 0, 0, 3, 0, 10, 18;
  1, 1, 0, 0, 6,  0, 18, 32;
  0, 1, 2, 0, 0, 10,  0, 32, 58;
  0, 0, 2, 3, 0,  0, 18,  0, 58, 103;
  1, 0, 0, 3, 6,  0,  0, 32,  0, 103, 184;
  ...
Row 4 = (1, 0, 2, 3) = termwise products of (1, 0, 1, 1) and (1, 1, 2, 3), where (1, 0, 1, 1) = the first 4 terms of A010060, reversed with offset 1.
(1, 1, 2, 3) = first 4 terms of A144026: (1, 1, 2, 3, 6, 10, 18, ...).

Crossrefs

Cf. A010060, A144026.

Sequence in context: A161515 A145580 A144219 * A019591 A353984 A341237

Adjacent sequences: A144024 A144025 A144026 * A144028 A144029 A144030

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 07 2008

Status

approved