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A240595 Look-and-Say table, where in row(n+1) the sorted list of distinct terms of row(n) is preceded by the list of numbers of their occurrences.

%I A240595 #7 Feb 16 2025 08:33:21
%S A240595 1,1,1,2,1,1,1,1,2,3,1,1,2,2,1,1,1,2,3,3,2,1,1,2,3,2,2,2,1,2,3,1,4,1,
%T A240595 1,2,3,3,1,1,1,1,2,3,4,4,1,2,1,1,2,3,4,3,2,1,2,1,2,3,4,2,3,2,1,1,2,3,
%U A240595 4,2,3,2,1,1,2,3,4,2,3,2,1,1,2,3,4,2
%N A240595 Look-and-Say table, where in row(n+1) the sorted list of distinct terms of row(n) is preceded by the list of numbers of their occurrences.
%C A240595 For n > 13: row(n) = row(13), see example.
%H A240595 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LookandSaySequence.html">Look and Say Sequence</a>
%H A240595 Wikipedia, <a href="http://en.wikipedia.org/wiki/Look-and-say_sequence">Look-and-say sequence</a>
%e A240595 .  1: [1] -> 1x1 -> [1 | 1] -> row(2)
%e A240595 .  2: [1,1] -> 2x1 -> [2 | 1] -> row(3)
%e A240595 .  3: [2,1] -> 1x1, 1x2 -> [1,1 | 1,2] -> row(4)
%e A240595 .  4: [1,1,1,2] -> 3x1, 1x2 -> [3,1 | 1,2] -> row(5)
%e A240595 .  5: [3,1,1,2] -> 2x1, 1x2, 1x3 -> [2,1,1 | 1,2,3] -> row(6)
%e A240595 .  6: [2,1,1,1,2,3] -> 3x1, 2x2, 1x3 -> [3,2,1 | 1,2,3] -> row(7)
%e A240595 .  7: [3,2,1,1,2,3] -> 2x1, 2x2, 2x3 -> [2,2,2 | 1,2,3] -> row(8)
%e A240595 .  8: [2,2,2,1,2,3] -> 1x1, 4x2, 1x3 -> [1,4,1 | 1,2,3] -> row(9)
%e A240595 .  9: [1,4,1,1,2,3] -> 3x1, 1x2, 1x3, 1x4 -> [3,1,1,1 | 1,2,3] -> row(10)
%e A240595 . 10: [3,1,1,1,1,2,3,4] -> 4x1, 1x2, 2x3, 1x4 -> [4,1,2,1 | 1,2,3,4]
%e A240595 . 11: [4,1,2,1,1,2,3,4] -> 3x1, 2x2, 1x3, 2x4 -> [3,2,1,2 | 1,2,3,4]
%e A240595 . 12: [3,2,1,2,1,2,3,4] -> 2x1, 3x2, 2x3, 1x4 -> [2,3,2,1 | 1,2,3,4]
%e A240595 . 13: [2,3,2,1,1,2,3,4] -> 2x1, 3x2, 2x3, 1x4 -> [2,3,2,1 | 1,2,3,4]
%e A240595 . 14: [2,3,2,1,1,2,3,4] = row(13).
%o A240595 (Haskell)
%o A240595 import Data.List (sort, group)
%o A240595 a240595 n k = a240595_tabf !! (n-1) !! (k-1)
%o A240595 a240595_row n = a240595_tabf !! (n-1)
%o A240595 a240595_tabf = iterate f [1] where
%o A240595    f xs = concat [map length zss, map head zss]
%o A240595           where zss = group $ sort xs
%Y A240595 Cf. A034002.
%K A240595 nonn,tabf
%O A240595 1,4
%A A240595 _Reinhard Zumkeller_, Apr 08 2014