This site is supported by donations to The OEIS Foundation.

 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 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 of 6.                    A194805            A135010 ------------------------------------------------------ 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 Cf. A135010, A138121, A138137, A141285, A194795-A194797, A194805. Sequence in context: A179218 A131119 A114901 * A113178 A108362 A171090 Adjacent sequences:  A194806 A194807 A194808 * A194810 A194811 A194812 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 | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .