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A309546 Number of even parts in the partitions of n into 5 parts. 0
0, 0, 0, 0, 0, 0, 1, 2, 5, 8, 15, 18, 27, 34, 49, 60, 81, 98, 127, 150, 190, 220, 271, 312, 376, 430, 511, 578, 677, 760, 881, 982, 1126, 1250, 1421, 1568, 1768, 1942, 2176, 2380, 2651, 2888, 3198, 3472, 3826, 4140, 4542, 4900, 5353, 5760, 6271, 6728, 7298 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..52.

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-1)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} (((i-1) mod 2) + ((j-1) mod 2) + ((k-1) mod 2) + ((l-1) mod 2) + ((n-i-j-k-l-1) mod 2)).

EXAMPLE

The partitions of n into 5 parts for n = 10, 11, ..

                                                       1+1+1+1+10

                                                        1+1+1+2+9

                                                        1+1+1+3+8

                                                        1+1+1+4+7

                                                        1+1+1+5+6

                                            1+1+1+1+9   1+1+2+2+8

                                            1+1+1+2+8   1+1+2+3+7

                                            1+1+1+3+7   1+1+2+4+6

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

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

                                1+1+1+1+8   1+1+2+2+7   1+1+3+4+5

                                1+1+1+2+7   1+1+2+3+6   1+1+4+4+4

                                1+1+1+3+6   1+1+2+4+5   1+2+2+2+7

                    1+1+1+1+7   1+1+1+4+5   1+1+3+3+5   1+2+2+3+6

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

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

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

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

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

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

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

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

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

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

  n  |     10          11          12          13          14        ...

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

a(n) |     15          18          27          34          49        ...

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

- Wesley Ivan Hurt, Sep 12 2019

MATHEMATICA

Table[Sum[Sum[Sum[Sum[Mod[i - 1, 2] + Mod[j - 1, 2] + Mod[k - 1, 2] + Mod[l - 1, 2] + Mod[n - i - j - k - l - 1, 2], {i, j, Floor[(n - j - k - l)/2]}], {j, k, Floor[(n - k - l)/3]}], {k, l, Floor[(n - l)/4]}], {l, Floor[n/5]}], {n, 0, 100}]

CROSSREFS

Sequence in context: A103077 A090980 A329603 * A261543 A307190 A183409

Adjacent sequences:  A309543 A309544 A309545 * A309547 A309548 A309549

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Aug 07 2019

STATUS

approved

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Last modified June 17 19:57 EDT 2021. Contains 345085 sequences. (Running on oeis4.)