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

0,1

Comments

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

Links

Table of n, a(n) for n=0..123.

Formula

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

Example

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;

Crossrefs

Sequence in context: A016410 A230412 A115361 * A325898 A117904 A259030

Adjacent sequences: A115355 A115356 A115357 * A115359 A115360 A115361

Keyword

easy,sign,tabl

Author

Paul Barry, Jan 21 2006

Status

approved