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A152205 Triangle read by rows, A000012 * A152204. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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)

LINKS

Table of n, a(n) for n=1..49.

FORMULA

A000012 * A152204 = partial sums of A152204 by columns.

EXAMPLE

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

Sequence in context: A070438 A070638 A236104 * A129861 A055491 A032523

Adjacent sequences:  A152202 A152203 A152204 * A152206 A152207 A152208

KEYWORD

nonn,tabf

AUTHOR

Gary W. Adamson, Nov 29 2008

STATUS

approved

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Last modified July 4 12:27 EDT 2022. Contains 355075 sequences. (Running on oeis4.)