A228169 Irregular triangle read by rows: T(n,k) is the number of binary pattern classes in the (10,n)-rectangular grid with k '1's and (10n-k) '0's: two patterns are in the same class if one of them can be obtained by a reflection or 180-degree rotation of the other.

1, 1, 5, 25, 60, 110, 126, 110, 60, 25, 5, 1, 1, 5, 55, 285, 1245, 3876, 9780, 19380, 31650, 41990, 46378, 41990, 31650, 19380, 9780, 3876, 1245, 285, 55, 5, 1, 1, 10, 130, 1070, 7080, 36102, 149785, 511260, 1468215, 3584050, 7523956, 13672690, 21646530, 29964990, 36386895, 38808456, 36386895, 29964990

Offset: 0

Author

Yosu Yurramendi, María Merino, Aug 14 2013

Keywords

• nonn
• tabf

Comments

The length of row n is 10*n+1.

Sum of rows (see example) gives A225834.

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, and triangle A228165 to A225830, triangle A228166 to A225831, triangle A228167 to A225832, and triangle A228168 to A225833.

Also the number of equivalence classes of ways of placing k 1 X 1 tiles in an n X 10 rectangle under all symmetry operations of the rectangle. - Christopher Hunt Gribble, Mar 01 2014

Examples

			Irregular triangle:
1
1  5  25   60  110   126    110     60      25       5       1
1  5  55  285 1245  3876   9780  19380   31650   41990   46378   41990...
1 10 130 1070 7080 36102 149785 511260 1468215 3584050 7523956 13672690 21646530 29964990 36386895 38808456 36386895 29964990 21646530 ...
		

Links

• Yosu Yurramendi, María Merino, Rows n = 0..16 of irregular triangle, flattened

Crossrefs

Cf. A225826-A225833, A005418, A034851, A226048, A226290, A225812, A228022, A228165-A228168.

Extensions

Definition corrected by María Merino, May 22 2017