cp's OEIS Frontend

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

%I A140760 #7 Feb 05 2018 15:18:15
%S A140760 2,6,12,14,24,26,30,28,48,50,54,62,52,58,96,56,60,98,102,110,126,100,
%T A140760 106,118,192,104,108,194,114,122,198,206,222,254,112,124,116,196,202,
%U A140760 214,238,384,120,200,204,386,210,218,390,230,246,398,414,446,510
%N A140760 Irregular table of natural numbers (read by columns) which can be mapped to the source partitions described in A053445 and A126441.
%C A140760 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.
%C A140760 The values for A140760 can also be generated by beginning with A140759 and repeatedly multiplying by two as follows:
%C A140760 2
%C A140760 ....6.....12......24.....48.....96
%C A140760 ..........14..........28........56
%C A140760 ..................26........52....
%C A140760 ..................30............60
%C A140760 .........................50.......
%C A140760 .........................54.......
%C A140760 .........................62.......
%C A140760 Note that the number of entries in each column is given by A053445.
%e A140760 The values of A140760 can be obtained by selecting the first even number on each applicable row of Table A126441.
%e A140760 Table A126441 begins
%e A140760 1.2.4..8.16.32.64.128.256.512.1024
%e A140760 ..3.5..9.17.33.65.129.257.513.1025
%e A140760 .......6.10.18.34..66.130.258..514
%e A140760 ....7.11.19.35.67.131.259.515.1027
%e A140760 ............12.20..36..68.132..260
%e A140760 .........13.21.37..69.133.261..517
%e A140760 ............14.22..38..70.134..262
%e A140760 ......15.23.39.71.135.263.519.1031
%e A140760 ...................24..40..72..136
%e A140760 ...............25..41..73.137..265
%e A140760 ...................26..42..74..138
%e A140760 ............27.43..75.139.267..523
%e A140760 .......................28..44...76
%e A140760 ...............29..45..77.141..269
%e A140760 ...................30..46..78..142
%e A140760 .........31.47.79.143.271.527.1039
%e A140760 ...........................48...80
%e A140760 .......................49..81..145
%e A140760 ...........................50...82
%e A140760 ...................51..83.147..275
%Y A140760 Cf. A000041, A000120, A002865, A053445, A125106, A126441, A140691, A140692, A140759.
%K A140760 nonn,tabf
%O A140760 1,1
%A A140760 _Alford Arnold_, May 28 2008