cp's OEIS Frontend

A228168 Irregular triangle read by rows: T(n,k) is the number of binary pattern classes in the (9,n)-rectangular grid with k '1's and (9n-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 A228168 #20 May 22 2017 08:06:58
%S A228168 1,1,5,20,44,66,66,44,20,5,1,1,5,45,208,792,2156,4704,7984,11034,
%T A228168 12190,11034,7984,4704,2156,792,208,45,5,1,1,10,106,785,4554,20556,
%U A228168 74828,223498,557599,1175574,2114550,3266415,4354188,5023464,5023464,4354188
%N A228168 Irregular triangle read by rows: T(n,k) is the number of binary pattern classes in the (9,n)-rectangular grid with k '1's and (9n-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 A228168 The length of row n is 9*n+1.
%C A228168 Sum of rows (see example) gives A225832.
%C A228168 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, triangle A228165 to A225830, triangle A228166 to A225831, and triangle A228167 to A225832.
%C A228168 Also the number of equivalence classes of ways of placing k 1 X 1 tiles in an n X 9 rectangle under all symmetry operations of the rectangle. - _Christopher Hunt Gribble_, Apr 27 2015
%H A228168 Yosu Yurramendi and María Merino, <a href="/A228168/b228168.txt">Rows n = 0..18 of irregular triangle, flattened</a>
%H A228168 Christopher Hunt Gribble, <a href="/A238009/a238009_1.cpp.txt">C++ program</a>
%e A228168 Irregular triangle:
%e A228168 1
%e A228168 1  5  20  44   66    66    44     20      5       1
%e A228168 1  5  45 208  792  2156  4704   7984  11034   12190   11034    7984  ...
%e A228168 1 10 106 785 4554 20556 74828 223498 557599 1175574 2114550 3266415 4354188 5023464 5023464 4354188 3266415 2114550 1175574 ...
%Y A228168 Cf. A225826-A225832, A005418, A034851, A226048, A226290, A225812, A228022, A228165, A228166, A228167.
%K A228168 nonn,tabf
%O A228168 0,3
%A A228168 _Yosu Yurramendi_, _María Merino_, Aug 14 2013
%E A228168 Definition corrected by _María Merino_, May 22 2017