|
%I #17 May 22 2017 08:18:44
%S 1,1,5,25,60,110,126,110,60,25,5,1,1,5,55,285,1245,3876,9780,19380,
%T 31650,41990,46378,41990,31650,19380,9780,3876,1245,285,55,5,1,1,10,
%U 130,1070,7080,36102,149785,511260,1468215,3584050,7523956,13672690,21646530,29964990,36386895,38808456,36386895,29964990
%N Irregular triangle read by rows: T(n,k) is the number of binary pattern classes in the (10,n)-rectangular grid with k '1's and (10n-k) '0's: two patterns are in the 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 10*n+1.
%C Sum of rows (see example) gives A225834.
%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, triangle A228166 to A225831, triangle A228167 to A225832, and triangle A228168 to A225833.
%C Also the number of equivalence classes of ways of placing k 1 X 1 tiles in an n X 10 rectangle under all symmetry operations of the rectangle. - _Christopher Hunt Gribble_, Mar 01 2014
%H Yosu Yurramendi, María Merino, <a href="/A228169/b228169.txt">Rows n = 0..16 of irregular triangle, flattened</a>
%e Irregular triangle:
%e 1
%e 1 5 25 60 110 126 110 60 25 5 1
%e 1 5 55 285 1245 3876 9780 19380 31650 41990 46378 41990...
%e 1 10 130 1070 7080 36102 149785 511260 1468215 3584050 7523956 13672690 21646530 29964990 36386895 38808456 36386895 29964990 21646530 ...
%Y Cf. A225826-A225833, A005418, A034851, A226048, A226290, A225812, A228022, A228165-A228168.
%K nonn,tabf
%O 0,3
%A _Yosu Yurramendi_, _María Merino_, Aug 14 2013
%E Definition corrected by _María Merino_, May 22 2017
|
