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A143810

Eigentriangle of A051731, the inverse Mobius transform.

1, 1, 1, 1, 0, 2, 1, 1, 0, 3, 1, 0, 0, 0, 5, 1, 1, 2, 0, 0, 6, 1, 0, 0, 0, 0, 0, 10, 1, 1, 0, 3, 0, 0, 0, 11, 1, 0, 2, 0, 0, 0, 0, 0, 16, 1, 1, 0, 0, 5, 0, 0, 0, 0, 19, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 1, 1, 2, 3, 0, 6, 0, 0, 0, 0, 0, 27, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40

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OFFSET

1,6

COMMENTS

Right border = A003238. Row sums = A003238 shifted one place to the left.

Sum of n-th row terms = rightmost term of next row. The sequence A003238: (1, 1, 2, 3, 5, 6, 10, 11,...) = the eigensequence of the inverse Mobius transform, A051731.

n-th row = termwise product of A051731 terms and the first n terms of A003238: (1, 1, 2, 3, 5, 6, 10, 11,...). Example: row 6 = (1, 1, 2, 0, 0, 6) = termwise product of (1, 1, 1, 0, 0, 1) and (1, 1, 2, 3, 5, 6).

LINKS

Table of n, a(n) for n=1..91.

FORMULA

Triangle read by rows, A051731 * (A003238 * 0^(n-k)); 1<=k<=n

EXAMPLE

First few rows of the triangle =

1, 1;

1, 0, 2;

1, 1, 0, 3;

1, 0, 0, 0, 5;

1, 1, 2, 0, 0, 6;

1, 0, 0, 0, 0, 0, 10;