A115358 Inverse of matrix (1,x)+(x,x^2) (expressed in Riordan array notation).

1, -1, 1, 0, 0, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, -1, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 0, 1

Offset: 0

Author

Paul Barry, Jan 21 2006

Keywords

• easy
• sign
• tabl

Comments

Row sums are A035263 (first Feigenbaum symbolic (or period-doubling) sequence). Columns are signed stretched Fredholm-Rueppel sequences. Inverse is A115356.

Examples

			Triangle begins
1;
-1, 1;
0, 0, 1;
1, -1, 0, 1;
0, 0, 0, 0, 1;
0, 0, -1, 0, 0, 1;
0, 0, 0, 0, 0, 0, 1;
-1, 1, 0, -1, 0, 0, 0, 1;
0, 0, 0, 0, 0, 0, 0, 0, 1;
0, 0, 0, 0, -1, 0, 0, 0, 0, 1;
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
		

Formula

Number triangle whose k-th column has g.f. x^k*sum{j>=0, (-1)^j*(x^(2j-1))^(k+1)}.