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

Author

Gary W. Adamson, Oct 25 2009

Keywords

• nonn
• tabl

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.

Examples

			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.

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.