A152205 Triangle read by rows, A000012 * A152204.

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, 36, 16, 4, 121, 81, 49, 25, 9, 1, 144, 100, 64, 36, 16, 4, 169, 121, 81, 49, 25, 9, 1

Offset: 1

Author

Gary W. Adamson, Nov 29 2008

Keywords

• nonn
• tabf

Comments

Row sums = A000292, the tetrahedral numbers.

From Gary W. Adamson, Feb 14 2010: (Start)

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.

M * [1, 2, 3, ...] = A001752: (1, 4, 11, 24, 46, 80, 130, ...).

M * [1, 3, 6, 10, ...] = A028346: (1, 4, 12, 28, 58, 108, ...). (End)

Examples

			First few rows of the triangle:
    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,  36,  16,   4;
  121,  81,  49,  25,   9,   1;
  144, 100,  64,  36,  16,   4;
  169, 121,  81,  49,  25,   9,   1;
  ...
		

Crossrefs

Cf. A152204, A000292.

Cf. A173277, A001752, A028346. - Gary W. Adamson, Feb 14 2010

Formula

A000012 * A152204 = partial sums of A152204 by columns.