cp's OEIS Frontend

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.

%I A228022 #22 May 22 2017 08:06:47
%S A228022 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,
%T A228022 1675,1675,1310,794,371,129,34,6,1,1,6,56,294,1253,3912,9808,19464,
%U A228022 31706,42116,46448,42116,31706,19464,9808,3912,1253,294,56,6,1
%N 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.
%C A228022 The length of row n is 5*n+1.
%C A228022 Sum of rows (see example) gives A225829.
%C A228022 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.
%C A228022 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
%H A228022 Yosu Yurramendi and María Merino, <a href="/A228022/b228022.txt">Rows n = 0..31 of irregular triangle, flattened</a>
%e A228022 Irregular triangle:
%e A228022 1
%e A228022 1 3  6   6    3    1
%e A228022 1 3 15  32   60   66   60    32    15     3     1
%e A228022 1 6 34 129  371  794 1310  1675  1675  1310   794   371   129
%e A228022   34 6 1
%e A228022 1 6 56 294 1253 3912 9808 19464 31706 42116 46448 42116 31706
%e A228022   19464 9808 3912 1253 294 56 6 1
%e A228022 ...
%Y A228022 Cf. A225826-A225829, A005418, A034851, A226048, A226290, A225812.
%K A228022 nonn,tabf
%O A228022 0,3
%A A228022 _Yosu Yurramendi_, _María Merino_, Aug 03 2013
%E A228022 Definition corrected by _María Merino_, May 22 2017