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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 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

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