A215655 Irregular triangle read by rows: reading the n-th row describes all the numbers seen in the triangle up to the end of the n-th row.

2, 2, 4, 2, 2, 4, 6, 2, 4, 4, 2, 6, 8, 2, 6, 4, 4, 6, 2, 8, 10, 2, 8, 4, 6, 6, 4, 8, 2, 10, 12, 2, 10, 4, 8, 6, 6, 8, 4, 10, 2, 12, 14, 2, 12, 4, 10, 6, 8, 8, 6, 10, 4, 12, 2, 14, 16, 2, 14, 4, 12, 6, 10, 8, 8, 10, 6, 12, 4, 14, 2, 16, 18, 2, 16, 4, 14, 6, 12, 8, 10, 10, 8, 12, 6, 14, 4, 16, 2, 18, 20, 2, 18, 4, 16, 6, 14, 8, 12, 10, 10, 12, 8, 14, 6, 16, 4, 18, 2, 20

Offset

1,1

Comments

Given the initial row "2 2", is the rest of the triangle forced? If not, should this version have an additional clause in the definition saying "lexicographically earliest, given the first row"?

Eric Angelini asks if there is a similar triangle (self-describing and infinite) that contains at least one odd number.

References

Eric Angelini, Posting to the Sequence Fans Mailing List, Oct 29 2012.

Links

Table of n, a(n) for n=1..110.

Example

Triangle begins:
2 2
4 2  2 4
6 2  4 4  2 6
8 2  6 4  4 6  2 8
10 2  8 4  6 6  4 8  2 10
12 2 10 4  8 6  6 8  4 10  2 12
14 2 12 4 10 6  8 8  6 10  4 12  2 14
16 2 14 4 12 6 10 8  8 10  6 12  4 14  2 16
18 2 16 4 14 6 12 8 10 10  8 12  6 14  4 16  2 18
20 2 18 4 16 6 14 8 12 10 10 12  8 14  6 16  4 18  2 20
...
Top line says: I see  two integers "2" so far
Next line says: I see four integers "2" and two integers "4" so far
Next line says: I see  six integers "2", four integers "4" and two integers "6" so far
etc.
The counts are thus cumulative. And the (easy-to-build) array infinite.

Crossrefs

Cf. A005150.

Sequence in context: A276604 A072301 A127171 * A118232 A115070 A064145

Adjacent sequences: A215652 A215653 A215654 * A215656 A215657 A215658

Keyword

nonn,tabf

Author

N. J. A. Sloane, Feb 17 2013

Status

approved