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A231428 Sorted and encoded binary matrices representing equivalence relations. 7
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 N X N 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 n X n matrices for a given n, truncate this sequence to the first A000110(n) elements.
LINKS
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: A088413 A372098 A090669 * A263660 A215822 A079374
KEYWORD
nonn
AUTHOR
Philippe Beaudoin, Nov 09 2013
STATUS
approved

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Last modified June 26 06:40 EDT 2024. Contains 373715 sequences. (Running on oeis4.)