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A309713 Sum of the odd parts appearing among the third largest parts of the partitions of n into 4 parts. 0
0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 7, 10, 17, 20, 27, 30, 42, 50, 67, 80, 102, 115, 144, 164, 200, 227, 270, 304, 363, 406, 474, 526, 603, 664, 761, 842, 959, 1051, 1179, 1282, 1434, 1561, 1737, 1888, 2088, 2252, 2480, 2672, 2928, 3148, 3432, 3680, 4009, 4289 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Table of n, a(n) for n=0..53.

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)} j * (j 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) |      3           3           7          10          17        ...

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

- Wesley Ivan Hurt, Sep 08 2019

MATHEMATICA

Table[Sum[Sum[Sum[j * Mod[j, 2], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 50}]

CROSSREFS

Sequence in context: A032060 A241385 A307736 * A153903 A331729 A095741

Adjacent sequences:  A309710 A309711 A309712 * A309714 A309715 A309716

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Aug 13 2019

STATUS

approved

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Last modified December 1 06:09 EST 2020. Contains 338833 sequences. (Running on oeis4.)