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A228354 Indices (k) of partitions in the list of compositions of j in colexicographic order, if 1<=k<=2^(j-1), j>=1. 4
1, 2, 4, 6, 8, 12, 16, 22, 24, 28, 32, 44, 48, 56, 64, 86, 88, 92, 96, 112, 120, 128, 172, 176, 184, 192, 220, 224, 240, 256, 342, 344, 348, 352, 368, 376, 384, 440, 448, 480, 496, 512, 684, 688, 696, 704, 732, 736, 752, 768, 880, 888, 896, 960, 992, 1024 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also where records occur in A228720.

Also triangle read by rows in which row j lists the indices of the partitions of j into parts greater than the smallest part of the partitions of j-1, in the list of compositions of j in colexicographic order. See A228525 and A211992.

The total number of terms in the first j rows of triangle is A000041(j), j >= 1.

Row j has length A187219(j).

Right border gives A000079.

LINKS

Table of n, a(n) for n=1..56.

FORMULA

a(n) = 1 + A194602(n-1).

A001511(a(n)) = A141285(n).

A000120(a(n)-1) = A207034(n).

EXAMPLE

For j = 5 consider the list of compositions of 5 in colexicographic order (see A228525). The indices of the partitions are 1, 2, 4, 6, 8, 12, 16 which are the first A000041(5) terms of this sequence, see below:

---------------------------------------------------------

.   Compositions                     Partitions

k      of 5                             of 5      n  a(n)

---------------------------------------------------------

1    1+1+1+1+1  * ............... *  1+1+1+1+1    1    1

2    2+1+1+1    * ............... *  2+1+1+1      2    2

3    1+2+1+1          ........... *  3+1+1        3    4

4    3+1+1      * .../ .......... *  2+2+1        4    6

5    1+1+2+1          / ......... *  4+1          5    8

6    2+2+1      * .../ /   ...... *  3+2          6   12

7    1+3+1            /   /   ... *  5            7   16

8    4+1        * .../   /   /

9    1+1+1+2            /   /

10   2+1+2             /   /

11   1+2+2            /   /

12   3+2        * .../   /

13   1+1+3              /

14   2+3               /

15   1+4              /

16   5          * .../

.

Written as an irregular triangle the sequence begins:

1;

2;

4;

6,8;

12,16;

22,24,28,32;

44,48,56,64;

86,88,92,96,112,120,128;

172,176,184,192,220,224,240,256;

342,344,348,352,368,376,384,440,448,480,496,512;

684,688,696,704,732,736,752,768,880,888,896,960,992,1024;

...

CROSSREFS

Cf. A000041, A187219, A211992, A228354, A228525, A228720.

Sequence in context: A061553 A138934 A008764 * A065386 A048951 A058629

Adjacent sequences:  A228351 A228352 A228353 * A228355 A228356 A228357

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Aug 20 2013

STATUS

approved

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Last modified February 16 20:45 EST 2019. Contains 320189 sequences. (Running on oeis4.)