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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The NxN binary matrix of an equivalence relation is perfectly defined by its upper-right triangle. We encode such a matrix with the (N*(N-1))/2 bit number obtained by joining together each line of the upper-right 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

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Last modified August 23 11:33 EDT 2014. Contains 245994 sequences.