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A144027 Eigentriangle by rows, T(n,k) = A010060(n-k+1)*A144026(k-1), 1<=k<=n. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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

The 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 A091967 A031135

Adjacent sequences:  A144024 A144025 A144026 * A144028 A144029 A144030

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Sep 07 2008

STATUS

approved

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Last modified December 21 17:16 EST 2014. Contains 252324 sequences.