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A160756 Triangle read by rows, infinite lower triangular Toeplitz matrix with A078008 in every column convolved with A001333.

%I A160756 #3 Mar 30 2012 17:25:34
%S A160756 1,0,1,2,0,1,2,2,0,3,6,2,2,0,7,10,6,2,6,0,17,22,10,6,6,14,0,41,42,22,
%T A160756 10,18,14,34,0,99,86,42,22,30,42,34,82,0,239,170,86,42,66,70,102,82,
%U A160756 198,0,577
%N A160756 Triangle read by rows, infinite lower triangular Toeplitz matrix with A078008 in every column convolved with A001333.
%C A160756 Row sums = A001333: (1, 1, 3, 7, 17, 41,...). Sum of n-th row terms = rightmost term of next row.
%F A160756 Let M = an infinite lower triangular Toeplitz matrix with A078008 (1, 0, 2, 2, 6, 10, 22, 42, 86, 170,...). Let Q = the eigensequence of that triangle prefaced with a 1: (1, 1, 1, 3, 7, 17,...) where A001333 = (1, 1, 3, 7, 17,...). The triangle = M * Q.
%e A160756 First few rows of the triangle =
%e A160756 1;
%e A160756 0, 1;
%e A160756 2, 0, 1;
%e A160756 2, 2, 0, 3;
%e A160756 6, 2, 2, 0, 7;
%e A160756 10, 6, 2, 6, 0, 17;
%e A160756 22, 10, 6, 6, 14, 0, 41;
%e A160756 42, 22, 10, 18, 14, 34, 0, 99;
%e A160756 86, 42, 22, 30, 42, 34, 82, 0, 239;
%e A160756 170, 86, 42, 66, 70, 102, 82, 198, 0, 577;
%e A160756 ...
%e A160756 Example: row 4 = (6, 2, 2, 0, 7) = (6, 2, 2, 0, 1) * (1, 1, 1, 3, 7).
%Y A160756 Cf. A078008, A001333
%K A160756 nonn,tabl
%O A160756 0,4
%A A160756 _Gary W. Adamson_, May 25 2009