The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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. 15
 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, 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, 2, 2, 2, 3, 2, 4, 1, 1, 3, 1, 4, 5, 5, 5, 1, 4, 4, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS 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). Other similar tables of unordered partitions: A036036, A036037, A080576, A080577 and A112798. LINKS Antti Karttunen, The rows 1..1023 of the table, flattened FORMULA a(n) = A227189(A227737(n),A227740(n)). EXAMPLE Rows are constructed as:   Row    n in   Runlengths  With one     Partial sums   The row sums    n    binary  collected   subtracted   of which give  to, i.e. is                 from lsb-   from all     terms on       a partition of                 to msb-end  except 1st   that row       of A227183(n)    1       "1"        [1]        [1]     1;             1    2      "10"      [1,1]      [1,0]     1, 1;          2    3      "11"        [2]        [2]     2;             2    4     "100"      [2,1]      [2,0]     2, 2;          4    5     "101"    [1,1,1]    [1,0,0]     1, 1, 1;       3    6     "110"      [1,2]      [1,1]     1, 2;          3    7     "111"        [3]        [3]     3;             3    8    "1000"      [3,1]      [3,0]     3, 3;          6    9    "1001"    [1,2,1]    [1,1,0]     1, 2, 2;       5   10    "1010"  [1,1,1,1]  [1,0,0,0]     1, 1, 1, 1;    4   11    "1011"    [2,1,1]    [2,0,0]     2, 2, 2;       6   12    "1100"      [2,2]      [2,1]     2, 3;          5   13    "1101"    [1,1,2]    [1,0,1]     1, 1, 2;       4   14    "1110"      [1,3]      [1,2]     1, 3;          4   15    "1111"        [4]        [4]     4;             4   16   "10000"      [4,1]      [4,0]     4, 4;          8 MATHEMATICA 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 *) PROG (Scheme) (define (A227739 n) (A227189bi (A227737 n) (A227740 n))) ;; The Scheme-code for A227189bi has been given in A227189. CROSSREFS Row sums: A227183, row products: A227184, the initial (smallest) term of each row: A136480, the last (largest) term: A227185. Cf. also A227189, A227738, A227736. Sequence in context: A081503 A176508 A241492 * A047971 A029432 A073426 Adjacent sequences:  A227736 A227737 A227738 * A227740 A227741 A227742 KEYWORD nonn,base,tabf AUTHOR Antti Karttunen, Jul 25 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 6 12:08 EDT 2020. Contains 333273 sequences. (Running on oeis4.)