A213057 - OEIS

%I #17 Feb 03 2019 20:55:05

%S 1,1,2,1,12,3,1,112,123,4,1,1112,112123,1234,5,1,11112,1112112123,

%T 1121231234,12345,6,1,111112,111121112112123,11121121231121231234,

%U 112123123412345,123456,7,1,1111112,111112111121112112123,11112111211212311121121231121231234,11121121231121231234112123123412345,112123123412345123456,1234567,8

%N 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.

%C Closely related to A004073 - see Kubo-Vakil.

%C 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.

%C Grytczuk calls this the "word Pascal triangle".

%H J. Grytczuk, <a href="http://dx.doi.org/10.1016/j.disc.2003.10.022">Another variation on Conway's recursive sequence</a>, Discr. Math. 282 (2004), 149-161.

%H T. Kubo and R. Vakil, <a href="http://dx.doi.org/10.1016/0012-365X(94)00303-Z">On Conway's recursive sequence</a>, Discr. Math. 152 (1996), 225-252.

%e Triangle begins

%e 1

%e 1 2

%e 1 12 3

%e 1 112 123 4

%e 1 1112 112123 1234 5

%e 1 11112 1112112123 1121231234 12345 6

%e 1 111112 111121112112123 11121121231121231234 112123123412345 123456 7

%e ...

%Y Cf. A004073, A007318.

%K nonn,tabl

%O 0,3

%A _N. J. A. Sloane_, Jun 03 2012