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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. 32

%I #22 May 22 2017 08:06:47

%S 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 1675,1675,1310,794,371,129,34,6,1,1,6,56,294,1253,3912,9808,19464,

%U 31706,42116,46448,42116,31706,19464,9808,3912,1253,294,56,6,1

%N 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 The length of row n is 5*n+1.

%C Sum of rows (see example) gives A225829.

%C 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 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 Yosu Yurramendi and María Merino, <a href="/A228022/b228022.txt">Rows n = 0..31 of irregular triangle, flattened</a>

%e Irregular triangle:

%e 1

%e 1 3 6 6 3 1

%e 1 3 15 32 60 66 60 32 15 3 1

%e 1 6 34 129 371 794 1310 1675 1675 1310 794 371 129

%e 34 6 1

%e 1 6 56 294 1253 3912 9808 19464 31706 42116 46448 42116 31706

%e 19464 9808 3912 1253 294 56 6 1

%e ...

%Y Cf. A225826-A225829, A005418, A034851, A226048, A226290, A225812.

%K nonn,tabf

%O 0,3

%A _Yosu Yurramendi_, _María Merino_, Aug 03 2013

%E Definition corrected by _María Merino_, May 22 2017

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)