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A166967 Triangle read by rows, (Sierpinski's gasket, A047999) * A166966 (diagonalized as a lower triangular matrix) 2
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A307884 A329221 A177858 * A136256 A283440 A337319
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Oct 25 2009
STATUS
approved

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Last modified May 22 09:57 EDT 2024. Contains 372745 sequences. (Running on oeis4.)