A271584 Irregular triangle read by rows: alternate (k-1)*k, k^2, for k = 0 to n.

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

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