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

%I A166967 #11 Jun 02 2025 02:09:50
%S A166967 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,
%T A166967 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,
%U A166967 135,1,1,2,3,0,0,0,0,66,67,135,204
%N A166967 Triangle read by rows, (Sierpinski's gasket, A047999) * A166966 (diagonalized as a lower triangular matrix).
%C A166967 An eigentriangle (a given triangle * its own eigensequence); in this case A047999 * A166966.
%C A166967 Triangle A166967 has the properties of: row sums = the eigensequence, A166966 and sum of n-th row terms = rightmost term of next row.
%F A166967 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,...].
%F A166967 Triangle A166967 = S * Q.
%e A166967 First few rows of the triangle =
%e A166967 1;
%e A166967 1, 1;
%e A166967 1, 1, 2, 3;
%e A166967 1, 0, 0, 0, 7;
%e A166967 1, 1, 0, 0, 7, 8;
%e A166967 1, 0, 2, 0, 7, 0, 17;
%e A166967 1, 1, 2, 3, 7, 8, 17, 27;
%e A166967 1, 0, 0, 0, 0, 0,..0,..0, 66;
%e A166967 1, 1, 0, 0, 0, 0,..0,..0, 66, 67;
%e A166967 1, 0, 2, 0, 0, 0,..0,..0, 66,..0, 135;
%e A166967 1, 1, 2, 3, 0, 0,..0,..0, 66, 67, 135, 204;
%e A166967 1, 0, 0, 0, 7, 0,..0,..0, 66,..0,...0,...0, 479;
%e A166967 1, 1, 0, 0, 7, 8,..0,..0, 66, 67,...0,...0, 479, 553
%e A166967 1, 0, 2, 0, 7, 0, 17,..0, 66,..0, 135,...0, 479,...0, 1182;
%e A166967 1, 1, 2, 3, 7, 8, 17, 27, 66, 67, 135, 204, 479, 553, 1182, 1189;
%e A166967 ...
%Y A166967 Cf. A047999, A166966.
%K A166967 nonn,tabl
%O A166967 0,6
%A A166967 _Gary W. Adamson_, Oct 25 2009