A228022 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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 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