login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A194809 Imbalance of the sum of largest parts of all partitions of n. 2
0, -2, 1, -5, 3, -12, 7, -25, 17, -47, 36, -88, 69, -155, 133, -262, 240, -439, 415, -717, 705, -1142, 1165, -1803, 1874, -2797, 2975, -4276, 4632, -6478, 7094, -9698, 10741, -14355, 16059, -21079, 23719, -30670, 34716, -44243, 50315, -63372 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Consider the three-dimensional structure of the shell model of partitions version "tree". Note that only the larges parts > 1 produce the imbalance. Note that every column where is located a largest part contains largest parts of the same size, thesame as a periodic table (see example). For more information see A135010.
LINKS
FORMULA
a(n) = Sum_{k=2..n} (-1)^(k-1)*A138137(k), n >= 2.
EXAMPLE
For n = 6 the illustration of the shell model with 6 shells shows an imbalance of largest parts (see below):
------------------------------------------------------
Partitions Tree Table 1.0
------------------------------------------------------
6 6 6 . . . . .
3+3 3 3 . . 3 . .
4+2 4 4 . . . 2 .
2+2+2 2 2 . 2 . 2 .
5+1 1 5 5 . . . . 1
3+2+1 1 3 3 . . 2 . 1
4+1+1 4 1 4 . . . 1 1
2+2+1+1 2 1 2 . 2 . 1 1
3+1+1+1 1 3 3 . . 1 1 1
2+1+1+1+1 2 1 2 . 1 1 1 1
1+1+1+1+1+1 1 1 1 1 1 1 1
------------------------------------------------------
The sum of largest parts > 1 on the left hand side is 23 and the sum of largest parts > 1 on the right hand side is 11, so a(6) = -23 + 11 = -12. On the other hand for n = 6 we have that 0 together with the first n-1 terms > 1 of A138137 are 0, 2, 3, 6, 8, 15 so a(6) = 0-2+3-6+8-15 = -12.
CROSSREFS
Sequence in context: A131119 A114901 A355562 * A113178 A108362 A171090
KEYWORD
sign
AUTHOR
Omar E. Pol, Feb 02 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 1 12:27 EST 2024. Contains 370433 sequences. (Running on oeis4.)