A165371 - OEIS

%I #8 Oct 02 2025 23:43:44

%S 1,40,1409,63740,5386897,948440084,397609974217

%N Number of slanted n X n (i=1..n)X(j=i..n+i-1) 1..4 arrays with all 1s connected, all 2s connected, all 3s connected, all 4s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, and 4 in the lower right corner.

%e Some solutions for n=4

%e ...1.1.1.2.........1.1.2.2.........1.1.1.2.........1.1.1.2......

%e .....1.1.4.4.........2.2.2.4.........1.3.2.2.........1.3.2.2....

%e .......1.1.4.4.........2.3.4.4.........3.3.3.3.........3.3.2.2..

%e .........3.4.4.4.........3.4.4.4.........3.3.3.4.........3.2.4.4

%e ------

%e ...1.1.2.2.........1.2.2.2.........1.4.4.2.........1.1.1.2......

%e .....1.1.4.4.........2.2.4.4.........4.4.4.4.........2.2.2.2....

%e .......4.4.4.4.........2.4.4.4.........4.4.4.4.........3.3.3.3..

%e .........3.4.4.4.........3.4.4.4.........3.3.4.4.........3.3.4.4

%e ------

%e ...1.1.2.2.........1.1.2.2.........1.1.1.2.........1.1.1.2......

%e .....1.2.2.2.........1.2.2.2.........1.1.1.1.........1.1.2.2....

%e .......2.3.2.2.........3.3.3.4.........3.3.3.4.........1.2.2.2..

%e .........3.2.2.4.........3.4.4.4.........3.3.4.4.........3.3.2.4

%K nonn

%O 2,2

%A _R. H. Hardin_, Sep 17 2009