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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.

%I A228165 #22 May 22 2017 08:06:52
%S A228165 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,
%T A228165 813,2196,4767,8070,11139,12300,11139,8070,4767,2196,813,218,48,6,1,1,
%U A228165 6,78,506,2706,10626,33814,86526,184239,326876,490908,624036,676732,624036,490908,326876,184239,86526,33814,10626,2706,506,78,6,1
%N 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.
%C A228165 The length of row n is 6*n+1.
%C A228165 Sum of rows (see example) gives A225830.
%C A228165 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.
%C A228165 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
%H A228165 Yosu Yurramendi, María Merino, <a href="/A228165/b228165.txt">Rows n = 0..20 of irregular triangle, flattened</a>
%e A228165 Irregular triangle:
%e A228165 1
%e A228165 1 3  9 10   9    3    1
%e A228165 1 3 21 55 135  198  246  198   135    55    21    3    1
%e A228165 1 6 48 18 813 2196 4767 8070 11139 12300 11139 8070 4767 2196 813 218 48 6 1
%Y A228165 Cf. A225826-A225830, A005418, A034851, A226048, A226290, A225812, A228022.
%K A228165 nonn,tabf
%O A228165 0,3
%A A228165 _Yosu Yurramendi_, _María Merino_, Aug 14 2013
%E A228165 Definition corrected by _María Merino_, May 22 2017