A228166 - OEIS

A228166

Irregular triangle read by rows: T(n,k) is the number of binary pattern classes in the (7,n)-rectangular grid with k '1's and (7n-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.

%I #18 May 22 2017 08:07:01

%S 1,1,4,12,19,19,12,4,1,1,4,28,94,266,508,777,868,777,508,266,94,28,4,

%T 1,1,8,65,363,1574,5231,13826,29454,51408,74130,88900,88900,74130,

%U 51408,29454,13826,5231,1574,363,65,8,1,1,8,106,832,5199,24648,94524,296296,777997,1727440,3282774,5369832,7608483,9362256,10032648,9362256

%N Irregular triangle read by rows: T(n,k) is the number of binary pattern classes in the (7,n)-rectangular grid with k '1's and (7n-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.

%C The length of row n is 7*n+1.

%C Sum of rows (see example) gives A225831.

%C 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.

%C Also the number of equivalence classes of ways of placing k 1 X 1 tiles in an n X 7 rectangle under all symmetry operations of the rectangle. - _Christopher Hunt Gribble_, Apr 24 2015

%H Yosu Yurramendi, María Merino, <a href="/A228166/b228166.txt">Rows n = 0..20 of irregular triangle, flattened</a>

%e Irregular triangle:

%e 1

%e 1 4 12 19 19 12 4 1

%e 1 4 28 94 266 508 777 868 777 508 266 94 28 4 1

%e 1 8 65 363 1574 5231 13826 29454 51408 74130 88900 88900 74130 51408 29454 13826 5231 1574 363 65 8 1

%Y Cf. A225826-A225829, A005418, A034851, A226048, A226290, A225812, A228022, A228165.

%K nonn,tabf

%O 0,3

%A _Yosu Yurramendi_, _María Merino_, Aug 14 2013

%E Definition corrected by _María Merino_, May 22 2017