

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 NxN 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 nxn 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


EXAMPLE

The 4x4 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 4x4 matrix corresponding to 25 = 0b011001 is:
1011
0100
1011
1011


CROSSREFS

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


KEYWORD

nonn


AUTHOR

Philippe Beaudoin, Nov 09 2013


STATUS

approved



