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%I #7 Dec 26 2023 12:29:29
%S 1,0,1,0,0,1,1,0,0,1,0,1,0,0,2,1,0,1,0,0,3,0,1,0,1,0,0,5,1,0,1,0,1,0,
%T 0,7,1,1,0,1,0,3,0,0,11,1,1,1,0,2,0,5,0,0,0,17,0,1,1,1,0,3,0,7,0,0,27,
%U 1,0,1,1,2,0,5,0,11,0,0,40
%N Triangle read by rows, A157423 * (A052284 * 0^(n-k))
%C Row sums = A052284 starting at n=1: (1, 1, 1, 2, 3, 5, 7, 11, 17,...). As a property of eigentriangles, sum of n-th row terms = rightmost term of next row.
%F Triangle read by rows, A157423 * (A052284 * 0^(n-k)). A157423 = an infinite lower triangular matrix with A005171 in every column. (A052284 * 0^(n-k)) = an infinite lower triangular matrix with A052284: (1, 1, 1, 1, 2, 3, 5, 7, 11, 17, 27,...) as the main diagonal and the rest zeros.
%e First few rows of the triangle =
%e 1;
%e 0, 1;
%e 0, 0, 1;
%e 1, 0, 0, 1;
%e 0, 1, 0, 0, 2;
%e 1, 0, 1, 0, 0, 3;
%e 0, 1, 0, 1, 0, 0, 5;
%e 1, 0, 1, 0, 2, 0, 0, 7;
%e 1, 1, 0, 1, 0, 3, 0, 0, 11;
%e 1, 1, 1, 0, 2, 0, 5,0, 0, 17;
%e 0, 1, 1, 1, 0, 3, 0, 7, 0, 0, 27;
%e 1, 0, 1, 1, 2, 0, 5, 0, 11, 0, 0, 40;
%e 0, 1, 0, 1, 2, 3, 0, 7, 0, 17, 0, 0, 61;
%e 1, 0, 1, 0, 2, 3, 5, 0, 11, 0, 27, 0, 0, 92;
%e ...
%e Example: row 5 = (0, 1, 0, 0, 2) = termwise products of (0, 1, 0, 0, 1) and
%e (1, 1, 1, 1, 2); where (0, 1, 0, 0, 2) = row 5 of triangle A157423 and
%e (1, 1, 1, 1, 2) = the first 5 terms of A052284.
%Y Cf. A157423, A005171, A052284
%K nonn,tabl
%O 1,15
%A _Gary W. Adamson_ & _Mats Granvik_, Feb 28 2009
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