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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.

Contribution 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

A152204, A000292

Cf. A173277, A001752, A028346 [From 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 May 28 10:48 EDT 2017. Contains 287240 sequences.