A140760 Irregular table of natural numbers (read by columns) which can be mapped to the source partitions described in A053445 and A126441.

2, 6, 12, 14, 24, 26, 30, 28, 48, 50, 54, 62, 52, 58, 96, 56, 60, 98, 102, 110, 126, 100, 106, 118, 192, 104, 108, 194, 114, 122, 198, 206, 222, 254, 112, 124, 116, 196, 202, 214, 238, 384, 120, 200, 204, 386, 210, 218, 390, 230, 246, 398, 414, 446, 510

Offset

1,1

Comments

Sequences A000041, A002865 and A053445 count numeric partitions. A125106 maps numeric partitions to the natural numbers and has A000120 elements per row. A126441 has A000041 elements per column and is a tabular arrangement of the natural numbers. A140691 is a rearrangement of table A126441. A140692 extracts the cyclic cases and has A002865 elements per column.

The values for A140760 can also be generated by beginning with A140759 and repeatedly multiplying by two as follows:

2

....6.....12......24.....48.....96

..........14..........28........56

..................26........52....

..................30............60

.........................50.......

.........................54.......

.........................62.......

Note that the number of entries in each column is given by A053445.

Links

Table of n, a(n) for n=1..55.

Example

The values of A140760 can be obtained by selecting the first even number on each applicable row of Table A126441.
Table A126441 begins
1.2.4..8.16.32.64.128.256.512.1024
..3.5..9.17.33.65.129.257.513.1025
.......6.10.18.34..66.130.258..514
....7.11.19.35.67.131.259.515.1027
............12.20..36..68.132..260
.........13.21.37..69.133.261..517
............14.22..38..70.134..262
......15.23.39.71.135.263.519.1031
...................24..40..72..136
...............25..41..73.137..265
...................26..42..74..138
............27.43..75.139.267..523
.......................28..44...76
...............29..45..77.141..269
...................30..46..78..142
.........31.47.79.143.271.527.1039
...........................48...80
.......................49..81..145
...........................50...82
...................51..83.147..275

Crossrefs

Cf. A000041, A000120, A002865, A053445, A125106, A126441, A140691, A140692, A140759.

Sequence in context: A190503 A320149 A346305 * A161922 A027863 A261978

Adjacent sequences: A140757 A140758 A140759 * A140761 A140762 A140763

Keyword

nonn,tabf

Author

Alford Arnold, May 28 2008

Status

approved