

A271584


Irregular triangle read by rows: alternate (k1)*k, k^2, for k = 0 to n.


1



0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 4, 0, 0, 2, 6, 0, 1, 4, 9, 0, 0, 2, 6, 12, 0, 1, 4, 9, 16, 0, 0, 2, 6, 12, 20, 0, 1, 4, 9, 16, 25, 0, 0, 2, 6, 12, 20, 30, 0, 1, 4, 9, 16, 25, 36, 0, 0, 2, 6, 12, 20, 30, 42, 0, 1, 4, 9, 16, 25, 36, 49
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OFFSET

0,9


COMMENTS

This is the irregular triangle e(n) mentioned in A269837.
Last number: 0, 0, 0, 1, 2, 4, 6, 9, 12, 16, 20, 25, ... = A002620 with a third initial 0.
Row sums: 0, 0, 0, 1, 2, 5, 8, 14, 20, 30, 40, ... = A006918 with three initial 0.
Columns: the sum of the first two terms is A000384(n).


LINKS

Table of n, a(n) for n=0..71.


EXAMPLE

Irregular triangle:
0,
0,
0, 0,
0, 1,
0, 0, 2,
0, 1, 4,
0, 0, 2, 6,
0, 1, 4, 9,
0, 0, 2, 6, 12,
0, 1, 4, 9, 16,
0, 0, 2, 6, 12, 20,
0, 1, 4, 9, 16, 25,
etc.


MATHEMATICA

Flatten[Transpose /@ Table[{k (k  1), k^2}, {n, 0, 7}, {k, 0, n}]] (* Michael De Vlieger, Apr 10 2016 *)


CROSSREFS

Cf. A000290, A000384, A002262, A006918, A161680, A269837.
Sequence in context: A257920 A258210 A258228 * A072737 A061290 A099096
Adjacent sequences: A271581 A271582 A271583 * A271585 A271586 A271587


KEYWORD

nonn,tabf


AUTHOR

Paul Curtz, Apr 10 2016


STATUS

approved



