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A309517 Sum of the odd parts in the partitions of n into 4 parts. 0
0, 0, 0, 0, 4, 3, 8, 9, 22, 26, 50, 59, 100, 114, 168, 197, 284, 329, 438, 504, 660, 748, 946, 1072, 1322, 1488, 1794, 2008, 2408, 2671, 3130, 3465, 4024, 4434, 5100, 5595, 6384, 6966, 7866, 8565, 9630, 10449, 11648, 12600, 13992, 15080, 16652, 17912, 19684 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..48.

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} (i * (i mod 2) + j * (j mod 2) + k * (k mod 2) + (n-i-j-k) * ((n-i-j-k) mod 2)).

EXAMPLE

Figure 1: The partitions of n into 4 parts for n = 8, 9, ..

                                                         1+1+1+9

                                                         1+1+2+8

                                                         1+1+3+7

                                                         1+1+4+6

                                             1+1+1+8     1+1+5+5

                                             1+1+2+7     1+2+2+7

                                 1+1+1+7     1+1+3+6     1+2+3+6

                                 1+1+2+6     1+1+4+5     1+2+4+5

                                 1+1+3+5     1+2+2+6     1+3+3+5

                     1+1+1+6     1+1+4+4     1+2+3+5     1+3+4+4

         1+1+1+5     1+1+2+5     1+2+2+5     1+2+4+4     2+2+2+6

         1+1+2+4     1+1+3+4     1+2+3+4     1+3+3+4     2+2+3+5

         1+1+3+3     1+2+2+4     1+3+3+3     2+2+2+5     2+2+4+4

         1+2+2+3     1+2+3+3     2+2+2+4     2+2+3+4     2+3+3+4

         2+2+2+2     2+2+2+3     2+2+3+3     2+3+3+3     3+3+3+3

--------------------------------------------------------------------------

  n  |      8           9          10          11          12        ...

--------------------------------------------------------------------------

a(n) |     22          26          50          59         100        ...

--------------------------------------------------------------------------

- Wesley Ivan Hurt, Sep 08 2019

MATHEMATICA

Table[Sum[Sum[Sum[(i * Mod[i, 2] + j * Mod[j, 2] + k * Mod[k, 2] + (n - i - j - k) * Mod[n - i - j - k, 2]), {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]

CROSSREFS

Sequence in context: A198576 A175047 A316688 * A105185 A165739 A196132

Adjacent sequences:  A309514 A309515 A309516 * A309518 A309519 A309520

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Aug 05 2019

STATUS

approved

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Last modified January 26 06:13 EST 2021. Contains 340434 sequences. (Running on oeis4.)