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Triangle read by rows in which row n contains a finite triangle as shown below.
5

%I #2 Mar 30 2012 17:33:59

%S 1,1,2,2,2,3,2,1,2,2,1,1,2,2,3,3,3,3,4,4,3,3,4,5,4,3,2,3,4,4,3,2,1,2,

%T 3,3,3,2,1,1,2,2,3,3,3,4,4,4,4,4,5,5,5,4,4,5,6,6,5,4,4,5,6,7,6,5,4,3,

%U 4,5,6,6,5,4,3,2,3,4,5,5,5,4,3,2,1,2,3,4,4,4,4,3,2,1,1,2,2,3,3,3,4,4,4,4,5

%N Triangle read by rows in which row n contains a finite triangle as shown below.

%e The main triangle begins:

%e 1,

%e 1,2,2,2,3,2,1,2,2,1,

%e 1,2,2,3,3,3,3,4,4,3,3,4,5,4,3,2,3,4,4,3,2,1,2,3,3,3,2,1,

%e 1,2,2,3,3,3,4,4,4,4,4,5,5,5,4,4,5,6,6,5,4,4,5,6,7,6,5,4,3,4,5,6,6,5,4,3,...

%e In which row 1 contains a vertex, only:

%e 1

%e Row 2 contains the triangle:

%e 1

%e 2,2

%e 2,3,2

%e 1,2,2,1

%e Row 3 contains the triangle:

%e 1

%e 2,2

%e 3,3,3

%e 3,4,4,3

%e 3,4,5,4,3

%e 2,3,4,4,3,2

%e 1,2,3,3,3,2,1

%e Row 4 contains the triangle:

%e 1

%e 2,2

%e 3,3,3

%e 4,4,4,4

%e 4,5,5,5,4

%e 4,5,6,6,5,4

%e 4,5,6,7,6,5,4

%e 3,4,5,6,6,5,4,3

%e 2,3,4,5,5,5,4,3,2

%e 1,2,3,4,4,4,4,3,2,1

%e Row 5 contains the triangle:

%e 1

%e 2,2

%e 3,3,3

%e 4,4,4,4

%e 5,5,5,5,5

%e 5,6,6,6,6,5

%e 5,6,7,7,7,6,5

%e 5,6,7,8,8,7,6,5

%e 5,6,7,8,9,8,7,6,5

%e 4,5,6,7,8,8,7,6,5,4

%e 3,4,5,6,7,7,7,6,5,4,3

%e 2,3,4,5,6,6,6,6,5,4,3,2

%e 1,2,3,4,5,5,5,5,5,4,3,2,1

%e And so on...

%K easy,nonn,tabf

%O 1,3

%A _Omar E. Pol_, Nov 09 2009