

A231428


Sorted and encoded binary matrices representing equivalence relations.


1



0, 1, 2, 4, 7, 8, 12, 16, 18, 25, 32, 33, 42, 52, 63, 64, 68, 80, 96, 116, 128, 130, 136, 160, 170, 193, 225, 256, 257, 264, 272, 281, 322, 338, 388, 396, 455, 512, 513, 514, 516, 519, 584, 588, 656, 658, 729, 800, 801, 874, 948, 1023, 1024
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OFFSET

1,3


COMMENTS

The N X N binary matrix of an equivalence relation is perfectly defined by its upperright triangle. We encode such a matrix with the (N*(N1))/2 bit number obtained by joining together each line of the upperright triangle. The numbers are converted to base 10.
This is an infinite sequence and can be used for arbitrarily large values of N. To enumerate the finite list of n X n matrices for a given n, truncate this sequence to the first A000110(n) elements.


LINKS

Philippe Beaudoin, Table of n, a(n) for n = 1..10000
Philippe Beaudoin, Python program to generate the sequence
Tilman Piesk, Illustrated list of the first 52 equivalence relations
Tilman Piesk, Nonsingleton blocks of the partitions of {1...8} in the same order.
Tilman Piesk, Permutations and partitions in the OEIS (Wikiversity)


EXAMPLE

The 4 X 4 equivalence matrices are represented by the first A000110(4) = 15 elements, that is: 0, 1, 2, 4, 7, 8, 12, 16, 18, 25, 32, 33, 42, 52, 63.
The 4 X 4 matrix corresponding to 25 = 0b011001 is:
1 0 1 1
0 1 0 0
1 0 1 1
1 0 1 1


CROSSREFS

Sequence in context: A233271 A088413 A090669 * A215822 A079374 A236217
Adjacent sequences: A231425 A231426 A231427 * A231429 A231430 A231431


KEYWORD

nonn,changed


AUTHOR

Philippe Beaudoin, Nov 09 2013


STATUS

approved



