A228354 Indices (k) of partitions in the list of compositions of j in colexicographic order, if 1<=k<=2^(j-1), j>=1.

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

Offset: 1

Author

Omar E. Pol, Aug 20 2013

Keywords

• nonn
• tabf

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.

Examples

			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.

Formula

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

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

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