



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
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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 leftshifted
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



