The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A196931 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A196931

Triangle read by rows in which row n lists in nondecreasing order the smallest part of every partition of n.
(history; published version)

#31 by Michael De Vlieger at Thu Dec 28 09:25:31 EST 2023

STATUS

proposed

approved

#30 by Michel Marcus at Thu Dec 28 03:46:29 EST 2023

STATUS

editing

proposed

#29 by Michel Marcus at Thu Dec 28 03:46:22 EST 2023

COMMENTS

If n >= 1, row n lists the smallest parts of every partition of n in the orden order produced by the shell model of partitions of A135010, hence row n lists the parts of the last section of the set of partitions of n, except the emergent parts (See A182699).

Row n has length A000041(n). Row sums give A046746. Right border of triangle gives A001477. Row n starts with A000041(n-1) ones, n >= 1.

EXAMPLE

0,

1,

1,2,

1,1,3,

1,1,1,2,4,

1,1,1,1,1,2,5,

1,1,1,1,1,1,1,2,2,3,6

1,1,1,1,1,1,1,1,1,1,1,2,2,3,7,

1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,8,

...

Row n has length A000041(n). Row sums give A046746. Right border of triangle gives A001477. Row n starts with A000041(n-1) ones, n >= 1.

...

STATUS

approved

editing

#28 by Charles R Greathouse IV at Sat Nov 30 21:30:37 EST 2013

COMMENTS

If n >= 1, row n lists the smallest parts of every partition of n in the orden produced by the shell model of partitions of A135010, hence row n lists the parts of the outer shell last section of the set of partitions of n, except the emergent parts (See A182699).

Discussion

Sat Nov 30

21:30

OEIS Server: https://oeis.org/edit/global/2071

#27 by Russ Cox at Fri Mar 30 17:34:09 EDT 2012

AUTHOR

_Omar E. Pol (info(AT)polprimos.com), _, Oct 21 2011

Discussion

Fri Mar 30

17:34

OEIS Server: https://oeis.org/edit/global/157

#26 by T. D. Noe at Fri Oct 21 13:55:28 EDT 2011

STATUS

proposed

approved

#25 by Omar E. Pol at Fri Oct 21 13:19:31 EDT 2011

STATUS

editing

proposed

#24 by Omar E. Pol at Fri Oct 21 13:19:28 EDT 2011

EXAMPLE

Row n has length A000041(n). The sum of row n is Row sums give A046746(n). Right border of triangle gives A001477. Row n starts with A000041(n-1) ones, n >= 1.

STATUS

proposed

editing

#23 by Omar E. Pol at Fri Oct 21 12:53:24 EDT 2011

STATUS

editing

proposed

#22 by Omar E. Pol at Fri Oct 21 12:53:20 EDT 2011

COMMENTS

If n >= 1, row n lists the smallest parts of every partition of n in the orden produced by the shell model of partitions of A135010, hence row n lists the parts of the outer shell of the partitions of n , except the emergent parts (See A182699).

STATUS

proposed

editing