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A309543 Number of odd parts in the partitions of n into 5 parts. 1
0, 0, 0, 0, 0, 5, 4, 8, 10, 17, 20, 32, 38, 56, 66, 90, 104, 137, 158, 200, 230, 285, 324, 393, 444, 530, 594, 697, 778, 905, 1004, 1153, 1274, 1450, 1594, 1802, 1972, 2213, 2414, 2690, 2924, 3242, 3512, 3873, 4184, 4595, 4948, 5410, 5812, 6330, 6784, 7362 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..51.

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 mod 2) + (j mod 2) + (k mod 2) + (l mod 2) + ((n-i-j-k-l) mod 2)).

G.f.: -x^5*(2*x^11-x^10+2*x^8+4*x^6-4*x^5+5*x^4-2*x^3+5*x^2-6*x+5) / ((x^2+1) *(x^2+x+1) *(x^2-x+1) *(x^4+x^3+x^2+x+1) *(x^4-x^3+x^2-x+1) *(x^4+1) *(x+1)^3 *(x-1)^5). - Alois P. Heinz, Aug 07 2019

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) |     20          32          38          56          66        ...

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

- Wesley Ivan Hurt, Sep 12 2019

MATHEMATICA

Table[Sum[Sum[Sum[Sum[Mod[i, 2] + Mod[j, 2] + Mod[k, 2] + Mod[l, 2] + Mod[n - i - j - k - l, 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, 50}]

CROSSREFS

Cf. A309516.

Sequence in context: A335846 A023845 A051555 * A187891 A086407 A160427

Adjacent sequences:  A309540 A309541 A309542 * A309544 A309545 A309546

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Aug 06 2019

STATUS

approved

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Last modified April 18 19:31 EDT 2021. Contains 343089 sequences. (Running on oeis4.)