A228022 Irregular triangle read by rows: T(n,k) is the number of binary pattern classes in the (5,n)-rectangular grid with k '1's and (5n-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, 6, 6, 3, 1, 1, 3, 15, 32, 60, 66, 60, 32, 15, 3, 1, 1, 6, 34, 129, 371, 794, 1310, 1675, 1675, 1310, 794, 371, 129, 34, 6, 1, 1, 6, 56, 294, 1253, 3912, 9808, 19464, 31706, 42116, 46448, 42116, 31706, 19464, 9808, 3912, 1253, 294, 56, 6, 1

Offset

0,3

Comments

The length of row n is 5*n+1.

Sum of rows (see example) gives A225829.

This triangle is to A225828 as Losanitsch's triangle A034851 is to A005418, triangle A226048 to A225826, triangle A226290 to A225827, and triangle A225812 to A225828.

Also the number of equivalence classes of ways of placing k 1 X 1 tiles in an n X 5 rectangle under all symmetry operations of the rectangle. - Christopher Hunt Gribble, Apr 24 2015

Links

Yosu Yurramendi and María Merino, Rows n = 0..31 of irregular triangle, flattened

Example

Irregular triangle:
1
1 3  6   6    3    1
1 3 15  32   60   66   60    32    15     3     1
1 6 34 129  371  794 1310  1675  1675  1310   794   371   129
  34 6 1
1 6 56 294 1253 3912 9808 19464 31706 42116 46448 42116 31706
  19464 9808 3912 1253 294 56 6 1
...

Crossrefs

Cf. A225826-A225829, A005418, A034851, A226048, A226290, A225812.

Sequence in context: A021277 A245215 A232569 * A323773 A309448 A354952

Adjacent sequences: A228019 A228020 A228021 * A228023 A228024 A228025

Keyword

nonn,tabf

Author

Yosu Yurramendi, María Merino, Aug 03 2013

Extensions

Definition corrected by María Merino, May 22 2017

Status

approved