A213057 Triangle read by rows: left edge is all 1's, right edge is 1, 2, 3, 4, ...; construct an internal entry by concatenating the two entries above it.

1, 1, 2, 1, 12, 3, 1, 112, 123, 4, 1, 1112, 112123, 1234, 5, 1, 11112, 1112112123, 1121231234, 12345, 6, 1, 111112, 111121112112123, 11121121231121231234, 112123123412345, 123456, 7, 1, 1111112, 111112111121112112123, 11112111211212311121121231121231234, 11121121231121231234112123123412345, 112123123412345123456, 1234567, 8

Offset: 0

Author

N. J. A. Sloane, Jun 03 2012

Keywords

• nonn
• tabl

Comments

Closely related to A004073 - see Kubo-Vakil.

After the 9th row of course we will encounter strings like 111...110, which is unsatisfactory. Still, the initial rows look nice and the sequence serves as a pointer to the Kubo-Vakil paper.

Grytczuk calls this the "word Pascal triangle".

Examples

			Triangle begins
1
1 2
1 12 3
1 112 123 4
1 1112 112123 1234 5
1 11112 1112112123 1121231234 12345 6
1 111112 111121112112123 11121121231121231234 112123123412345 123456 7
...
		

Links

• J. Grytczuk, Another variation on Conway's recursive sequence, Discr. Math. 282 (2004), 149-161.
• T. Kubo and R. Vakil, On Conway's recursive sequence, Discr. Math. 152 (1996), 225-252.

Crossrefs

Cf. A004073, A007318.