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%I #9 Mar 11 2014 01:34:18
%S 1,2,1,3,0,1,2,0,1,1,4,0,0,1,1
%N A shell model of partitions as a table of partitions.
%C This array read by antidiagonals is a table of partitions for all integers.
%C For another version but as a binary code see A182741.
%C For more information see A135010 and A138121 which are the main entries for this sequence.
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpatru.jpg">Illustration of the shell model of partitions for 1..6 (2D-3D view)</a>
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpa2dt.jpg">Illustration of the shell model of partitions for 1..10 (2D view)</a>
%H Omar E. Pol <a href="http://www.polprimos.com/imagenespub/polpa3dt.jpg">Illustration of the shell model of partitions for 1..9 (3D view)</a>
%e For the numbers 1..6 the shell model of partitions has 6 shells. The model as a table looks like this:
%e 1 1 1 1 1 1
%e 2 . 1 1 1 1
%e 3 . . 1 1 1
%e 2 . 2 . 1 1
%e 4 . . . 1 1
%e 3 . . 2 . 1
%e 5 . . . . 1
%e 2 . 2 . 2 .
%e 4 . . . 2 .
%e 3 . . 3 . .
%e 6 . . . . .
%e Then replace the dots by zeros.
%e Remarks: one number by column, for example 23 is located only in a column, not in two columns.
%e The table looks like this:
%e 1 1 1 1 1 1
%e 2 0 1 1 1 1
%e 3 0 0 1 1 1
%e 2 0 2 0 1 1
%e 4 0 0 0 1 1
%e 3 0 0 2 0 1
%e 5 0 0 0 0 1
%e 2 0 2 0 2 0
%e 4 0 0 0 2 0
%e 3 0 0 3 0 0
%e 6 0 0 0 0 0
%e Array begins:
%e 1,1,1,1,1,1,
%e 2,0,1,1,1,
%e 3,0,0,1,
%e 2,0,2,
%e 4,0,
%e 3,
%Y Cf. A135010, A138121, A182741, A182742, A182743.
%K nonn,tabl,more
%O 1,2
%A _Omar E. Pol_, Nov 30 2010
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