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%I #7 Jun 05 2021 06:48:53
%S 1,4,9,1,16,4,25,9,1,36,16,4,49,25,9,1,64,36,16,4,81,49,25,9,1,100,64,
%T 36,16,4,121,81,49,25,9,1,144,100,64,36,16,4,169,121,81,49,25,9,1
%N Triangle read by rows, A000012 * A152204.
%C Row sums = A000292, the tetrahedral numbers.
%C From _Gary W. Adamson_, Feb 14 2010: (Start)
%C Let the triangle = M. Then lim_{n->inf} M^n = A173277 as a left-shifted vector: (1, 4, 13, 32, 74, 152, 298, ...) = A(x), where A(x) satisfies A000290 = A(x)/A(x^2), A000290 = integer squares.
%C M * [1, 2, 3, ...] = A001752: (1, 4, 11, 24, 46, 80, 130, ...).
%C M * [1, 3, 6, 10, ...] = A028346: (1, 4, 12, 28, 58, 108, ...). (End)
%F A000012 * A152204 = partial sums of A152204 by columns.
%e First few rows of the triangle:
%e 1;
%e 4;
%e 9, 1;
%e 16, 4;
%e 25, 9, 1;
%e 36, 16, 4;
%e 49, 25, 9, 1;
%e 64, 36, 16, 4;
%e 81, 49, 25, 9, 1;
%e 100, 64, 36, 16, 4;
%e 121, 81, 49, 25, 9, 1;
%e 144, 100, 64, 36, 16, 4;
%e 169, 121, 81, 49, 25, 9, 1;
%e ...
%Y Cf. A152204, A000292.
%Y Cf. A173277, A001752, A028346. - _Gary W. Adamson_, Feb 14 2010
%K nonn,tabf
%O 1,2
%A _Gary W. Adamson_, Nov 29 2008
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