login
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.
0

%I #22 May 04 2013 07:16:56

%S 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,

%T 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,

%U 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

%N 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.

%C 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"?

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

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

%e Triangle begins:

%e 2 2

%e 4 2 2 4

%e 6 2 4 4 2 6

%e 8 2 6 4 4 6 2 8

%e 10 2 8 4 6 6 4 8 2 10

%e 12 2 10 4 8 6 6 8 4 10 2 12

%e 14 2 12 4 10 6 8 8 6 10 4 12 2 14

%e 16 2 14 4 12 6 10 8 8 10 6 12 4 14 2 16

%e 18 2 16 4 14 6 12 8 10 10 8 12 6 14 4 16 2 18

%e 20 2 18 4 16 6 14 8 12 10 10 12 8 14 6 16 4 18 2 20

%e ...

%e Top line says: I see two integers "2" so far

%e Next line says: I see four integers "2" and two integers "4" so far

%e Next line says: I see six integers "2", four integers "4" and two integers "6" so far

%e etc.

%e The counts are thus cumulative. And the (easy-to-build) array infinite.

%Y Cf. A005150.

%K nonn,tabf

%O 1,1

%A _N. J. A. Sloane_, Feb 17 2013