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A152205 Triangle read by rows, A000012 * A152204 4

%I

%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 Contribution from _Gary W. Adamson_, Feb 14 2010: (Start)

%C Let the triangle = M. Then Lim_{n->inf} M^n = A173277 as a left-shifted

%C vector: (1, 4, 13, 32, 74, 152, 298,...) = A(x), where A(x) satisfies

%C 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 A152204, A000292

%Y Cf. A173277, A001752, A028346 [From _Gary W. Adamson_, Feb 14 2010]

%K nonn,tabf

%O 1,2

%A _Gary W. Adamson_, Nov 29 2008

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Last modified May 6 00:41 EDT 2021. Contains 343579 sequences. (Running on oeis4.)