A228167 Irregular triangle read by rows: T(n,k) is the number of binary pattern classes in the (8,n)-rectangular grid with k '1's and (8n-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, 4, 16, 28, 38, 28, 16, 4, 1, 1, 4, 36, 140, 476, 1092, 2044, 2860, 3270, 2860, 2044, 1092, 476, 140, 36, 4, 1, 1, 8, 84, 536, 2770, 10808, 34116, 87144, 185071, 328208, 492392, 625968, 678524, 625968, 492392, 328208, 185071, 87144, 34116, 10808, 2770, 536, 84, 8, 1

Offset: 0

Author

Yosu Yurramendi, María Merino, Aug 14 2013

Keywords

• nonn
• tabf

Comments

The length of row n is 8*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, and triangle A228166 to A225831.

Also the number of equivalence classes of ways of placing k 1 X 1 tiles in an n X 8 rectangle under all symmetry operations of the rectangle. - Christopher Hunt Gribble, Feb 28 2014

Examples

			Irregular triangle:
1
1 4  16   28   38    28     16      4       1
1 4  36  140  476  1092   2044   2860    3270    2860     2044   1092 ...
1 8  84  536 2770 10808  34116  87144  185071  328208   492392 625968   678524   625968    492392   ...
		

Links

• Yosu Yurramendi and María Merino, Rows n = 0..20 of irregular triangle, flattened

Crossrefs

Cf. A225826-A225831, A005418, A034851, A226048, A226290, A225812, A228022, A228165, A228166.

Extensions

Definition corrected by María Merino, May 22 2017