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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 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, 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 * A263660 A215822 A079374 Adjacent sequences:  A231425 A231426 A231427 * A231429 A231430 A231431 KEYWORD nonn AUTHOR Philippe Beaudoin, Nov 09 2013 STATUS approved

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Last modified December 15 11:05 EST 2018. Contains 318148 sequences. (Running on oeis4.)