A228165 Irregular triangle read by rows: T(n,k) is the number of binary pattern classes in the (6,n)-rectangular grid with k '1's and (6n-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, 3, 9, 10, 9, 3, 1, 1, 3, 21, 55, 135, 198, 246, 198, 135, 55, 21, 3, 1, 1, 6, 48, 218, 813, 2196, 4767, 8070, 11139, 12300, 11139, 8070, 4767, 2196, 813, 218, 48, 6, 1, 1, 6, 78, 506, 2706, 10626, 33814, 86526, 184239, 326876, 490908, 624036, 676732, 624036, 490908, 326876, 184239, 86526, 33814, 10626, 2706, 506, 78, 6, 1

Offset

0,3

Comments

The length of row n is 6*n+1.

Sum of rows (see example) gives A225830.

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, and triangle A228022 to A225829.

Also the number of equivalence classes of ways of placing k 1 X 1 tiles in an n X 6 rectangle under all symmetry operations of the rectangle. - Christopher Hunt Gribble, Apr 24 2015

Links

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

Example

Irregular triangle:
1
1 3  9 10   9    3    1
1 3 21 55 135  198  246  198   135    55    21    3    1
1 6 48 18 813 2196 4767 8070 11139 12300 11139 8070 4767 2196 813 218 48 6 1

Crossrefs

Cf. A225826-A225830, A005418, A034851, A226048, A226290, A225812, A228022.

Sequence in context: A038227 A080292 A273893 * A114022 A181862 A329560

Adjacent sequences: A228162 A228163 A228164 * A228166 A228167 A228168

Keyword

nonn,tabf

Author

Yosu Yurramendi, María Merino, Aug 14 2013

Extensions

Definition corrected by María Merino, May 22 2017

Status

approved