A228168 Irregular triangle read by rows: T(n,k) is the number of binary pattern classes in the (9,n)-rectangular grid with k '1's and (9n-k) '0's: two patterns are in same class if one of them can be obtained by a reflection or 180-degree rotation of the other.

1, 1, 5, 20, 44, 66, 66, 44, 20, 5, 1, 1, 5, 45, 208, 792, 2156, 4704, 7984, 11034, 12190, 11034, 7984, 4704, 2156, 792, 208, 45, 5, 1, 1, 10, 106, 785, 4554, 20556, 74828, 223498, 557599, 1175574, 2114550, 3266415, 4354188, 5023464, 5023464, 4354188

Offset: 0

Author

Yosu Yurramendi, María Merino, Aug 14 2013

Keywords

• nonn
• tabf

Comments

The length of row n is 9*n+1.

Sum of rows (see example) gives A225832.

This triangle is to A225828 as Losanitsch's triangle A034851 is to A005418, triangle A226048 to A225826, triangle A226290 to A225827, triangle A225812 to A225828, triangle A228022 to A225829, triangle A228165 to A225830, triangle A228166 to A225831, and triangle A228167 to A225832.

Also the number of equivalence classes of ways of placing k 1 X 1 tiles in an n X 9 rectangle under all symmetry operations of the rectangle. - Christopher Hunt Gribble, Apr 27 2015

Examples

			Irregular triangle:
1
1  5  20  44   66    66    44     20      5       1
1  5  45 208  792  2156  4704   7984  11034   12190   11034    7984  ...
1 10 106 785 4554 20556 74828 223498 557599 1175574 2114550 3266415 4354188 5023464 5023464 4354188 3266415 2114550 1175574 ...
		

Links

• Yosu Yurramendi and María Merino, Rows n = 0..18 of irregular triangle, flattened
• Christopher Hunt Gribble, C++ program

Crossrefs

Cf. A225826-A225832, A005418, A034851, A226048, A226290, A225812, A228022, A228165, A228166, A228167.

Extensions

Definition corrected by María Merino, May 22 2017