This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A227739 #25 Jan 20 2020 21:42:17
%S A227739 1,1,1,2,2,2,1,1,1,1,2,3,3,3,1,2,2,1,1,1,1,2,2,2,2,3,1,1,2,1,3,4,4,4,
%T A227739 1,3,3,1,1,2,2,2,3,3,2,2,2,2,1,1,1,1,1,1,2,2,2,3,3,3,3,4,1,2,3,1,1,1,
%U A227739 2,2,2,3,2,4,1,1,3,1,4,5,5,5,1,4,4,1,1
%N A227739 Irregular table where row n lists in nondecreasing order the parts of unordered partition encoded in the runlengths of binary expansion of n; nonzero terms of A227189.
%C A227739 Row n has A005811(n) elements. Each row contains a unique (unordered) partition of some integer, and all possible partitions of finite natural numbers eventually occur. The first partition that sums to k occurs at row A227368(k) and the last at row A000225(k).
%C A227739 Other similar tables of unordered partitions: A036036, A036037, A080576, A080577 and A112798.
%H A227739 Antti Karttunen, <a href="/A227739/b227739.txt">The rows 1..1023 of the table, flattened</a>
%F A227739 a(n) = A227189(A227737(n),A227740(n)).
%e A227739 Rows are constructed as:
%e A227739 Row n in Runlengths With one Partial sums The row sums
%e A227739 n binary collected subtracted of which give to, i.e. is
%e A227739 from lsb- from all terms on a partition of
%e A227739 to msb-end except 1st that row of A227183(n)
%e A227739 1 "1" [1] [1] 1; 1
%e A227739 2 "10" [1,1] [1,0] 1, 1; 2
%e A227739 3 "11" [2] [2] 2; 2
%e A227739 4 "100" [2,1] [2,0] 2, 2; 4
%e A227739 5 "101" [1,1,1] [1,0,0] 1, 1, 1; 3
%e A227739 6 "110" [1,2] [1,1] 1, 2; 3
%e A227739 7 "111" [3] [3] 3; 3
%e A227739 8 "1000" [3,1] [3,0] 3, 3; 6
%e A227739 9 "1001" [1,2,1] [1,1,0] 1, 2, 2; 5
%e A227739 10 "1010" [1,1,1,1] [1,0,0,0] 1, 1, 1, 1; 4
%e A227739 11 "1011" [2,1,1] [2,0,0] 2, 2, 2; 6
%e A227739 12 "1100" [2,2] [2,1] 2, 3; 5
%e A227739 13 "1101" [1,1,2] [1,0,1] 1, 1, 2; 4
%e A227739 14 "1110" [1,3] [1,2] 1, 3; 4
%e A227739 15 "1111" [4] [4] 4; 4
%e A227739 16 "10000" [4,1] [4,0] 4, 4; 8
%t A227739 Table[Function[b, Accumulate@ Prepend[If[Length@ b > 1, Rest[b] - 1, {}], First@ b]]@ Map[Length, Split@ Reverse@ IntegerDigits[n, 2]], {n, 34}] // Flatten (* _Michael De Vlieger_, May 09 2017 *)
%o A227739 (Scheme) (define (A227739 n) (A227189bi (A227737 n) (A227740 n))) ;; The Scheme-code for A227189bi has been given in A227189.
%Y A227739 Row sums: A227183, row products: A227184, the initial (smallest) term of each row: A136480, the last (largest) term: A227185.
%Y A227739 Cf. also A227189, A227738, A227736.
%K A227739 nonn,base,tabf
%O A227739 1,4
%A A227739 _Antti Karttunen_, Jul 25 2013