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%I #14 Dec 10 2018 08:53:08
%S 1,2,1,3,1,3,4,2,3,7,5,2,3,7,16,6,3,6,7,16,33,7,3,6,7,16,33,71,8,4,6,
%T 14,16,33,71,143,9,4,9,14,16,33,71,143,295,10,5,9,14,32,33,71,143,295,
%U 594
%N Triangle read by rows, A010766 convolved with A014668 (diagonalized as an infinite lower triangular matrix)
%C This is an eigentriangle (i.e., a lower triangular matrix * a diagonalized version of its eigensequence); A014668 is the eigensequence of triangle A010766.
%C Row sums = A014668 starting (1, 3, 7, 16, 33, 71, 143, ...).
%C Sum of n-th row terms = rightmost term of next row.
%H G. C. Greubel, <a href="/A163313/b163313.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F Equals M * Q as infinite lower triangular matrices, where M = triangle A010766 and Q = a matrix with A014668: (1, 1, 3, 7, 16, 33, 71, 143, ...) as the main diagonal and the rest zeros.
%e First few rows of the triangle =
%e 1;
%e 2, 1;
%e 3, 1, 3;
%e 4, 2, 3, 7;
%e 5, 2, 3, 7, 16;
%e 6, 3, 6, 7, 16, 33;
%e 7, 3, 6, 7, 16, 33 71;
%e 8, 4, 6, 14, 16, 33, 71, 143;
%e 9, 4, 9, 14, 16, 33, 71, 143, 295;
%e 10, 5, 9, 14, 32, 33, 71, 143, 295, 594;
%e 11, 5, 9, 14, 32, 33, 71, 143, 295, 594, 1206;
%e 12, 6, 12, 21, 32, 66, 71, 143, 295, 594, 1206, 2413;
%e ...
%e Example: row 4 = (4, 2, 3, 7) = (4, 2, 1, 1) * (1, 1, 3, 7).
%t a[1] = 1; a[n_] := a[n] = Sum[Sum[a[d], {d, Divisors[k]}], {k, 1, n -1}];
%t Table[Floor[n/k]* a[k], {n, 1, 5}, {k, 1, n}]//Flatten (* _G. C. Greubel_, Dec 18 2016 *)
%Y Cf. A010766, A014668.
%K nonn,tabl
%O 1,2
%A _Gary W. Adamson_ & _Mats Granvik_, Jul 30 2009
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