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A228167 Irregular triangle read by rows: T(n,k) is the number of binary pattern classes in the (8,n)-rectangular grid with k '1's and (8n-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. 24

%I

%S 1,1,4,16,28,38,28,16,4,1,1,4,36,140,476,1092,2044,2860,3270,2860,

%T 2044,1092,476,140,36,4,1,1,8,84,536,2770,10808,34116,87144,185071,

%U 328208,492392,625968,678524,625968,492392,328208,185071,87144,34116,10808,2770,536,84,8,1

%N Irregular triangle read by rows: T(n,k) is the number of binary pattern classes in the (8,n)-rectangular grid with k '1's and (8n-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 8*n+1.

%C Sum of rows (see example) gives A225832.

%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, triangle A228165 to A225830, and triangle A228166 to A225831.

%C Also the number of equivalence classes of ways of placing k 1 X 1 tiles in an n X 8 rectangle under all symmetry operations of the rectangle. - _Christopher Hunt Gribble_, Feb 28 2014

%H Yosu Yurramendi and María Merino, <a href="/A228167/b228167.txt">Rows n = 0..20 of irregular triangle, flattened</a>

%e Irregular triangle:

%e 1

%e 1 4 16 28 38 28 16 4 1

%e 1 4 36 140 476 1092 2044 2860 3270 2860 2044 1092 ...

%e 1 8 84 536 2770 10808 34116 87144 185071 328208 492392 625968 678524 625968 492392 ...

%Y Cf. A225826-A225831, A005418, A034851, A226048, A226290, A225812, A228022, A228165, A228166.

%K nonn,tabf

%O 0,3

%A _Yosu Yurramendi_, _María Merino_, Aug 14 2013

%E Definition corrected by _María Merino_, May 22 2017

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Last modified April 5 22:47 EDT 2020. Contains 333260 sequences. (Running on oeis4.)