A166967 Triangle read by rows, (Sierpinski's gasket, A047999) * A166966 (diagonalized as a lower triangular matrix)

1, 1, 1, 1, 0, 2, 1, 1, 2, 3, 1, 0, 0, 0, 7, 1, 1, 0, 0, 7, 8, 1, 0, 2, 0, 7, 0, 17, 1, 1, 2, 3, 7, 8, 17, 27, 1, 0, 0, 0, 0, 0, 0, 0, 66, 1, 1, 0, 0, 0, 0, 0, 0, 66, 67, 1, 0, 2, 0, 0, 0, 0, 0, 66, 0, 135, 1, 1, 2, 3, 0, 0, 0, 0, 66, 67, 135, 204

Offset

0,6

Comments

An eigentriangle (a given triangle * its own eigensequence); in this case A047999 * A166966.

Triangle A166967 has the properties of: row sums = the eigensequence, A166966 and sum of n-th row terms = rightmost term of next row.

Links

Table of n, a(n) for n=0..77.

Formula

Let Sierpinski's gasket, A047999 = S; and Q = the eigensequence of A047999 prefaced with a 1: (1, 1, 2, 3, 7, 8, 17,...) then diagonalized as an infinite lower triangular matrix: [1; 0,1; 0,0,2; 0,0,0,3; 0,0,0,0,7,...].

Triangle A166967 = S * Q.

Example

First few rows of the triangle =
1;
1, 1;
1, 1, 2, 3;
1, 0, 0, 0, 7;
1, 1, 0, 0, 7, 8;
1, 0, 2, 0, 7, 0, 17;
1, 1, 2, 3, 7, 8, 17, 27;
1, 0, 0, 0, 0, 0,..0,..0, 66;
1, 1, 0, 0, 0, 0,..0,..0, 66, 67;
1, 0, 2, 0, 0, 0,..0,..0, 66,..0, 135;
1, 1, 2, 3, 0, 0,..0,..0, 66, 67, 135, 204;
1, 0, 0, 0, 7, 0,..0,..0, 66,..0,...0,...0, 479;
1, 1, 0, 0, 7, 8,..0,..0, 66, 67,...0,...0, 479, 553
1, 0, 2, 0, 7, 0, 17,..0, 66,..0, 135,...0, 479,...0, 1182;
1, 1, 2, 3, 7, 8, 17, 27, 66, 67, 135, 204, 479, 553, 1182, 1189;
...

Crossrefs

Cf. A047999, A166966.

Sequence in context: A307884 A329221 A177858 * A136256 A283440 A337319

Adjacent sequences: A166964 A166965 A166966 * A166968 A166969 A166970

Keyword

nonn,tabl

Author

Gary W. Adamson, Oct 25 2009

Status

approved