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

0,3

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".

Links

Table of n, a(n) for n=0..35.

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.

Example

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
...

Crossrefs

Cf. A004073, A007318.

Sequence in context: A358111 A211099 A058734 * A103187 A286670 A288433

Adjacent sequences: A213054 A213055 A213056 * A213058 A213059 A213060

Keyword

nonn,tabl

Author

N. J. A. Sloane, Jun 03 2012

Status

approved