login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A309519 Sum of the even parts in the partitions of n into 4 parts. 0
0, 0, 0, 0, 0, 2, 4, 12, 18, 28, 40, 62, 80, 120, 154, 208, 260, 334, 408, 522, 620, 764, 902, 1090, 1270, 1512, 1742, 2042, 2324, 2694, 3050, 3510, 3944, 4476, 4998, 5640, 6252, 7020, 7752, 8634, 9490, 10502, 11494, 12684, 13816, 15160, 16468, 17996, 19484 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

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-1) mod 2) + j * ((j-1) mod 2) + k * ((k-1) mod 2) + (n-i-j-k) * ((n-i-j-k-1) 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) |     18          28          40          62          80        ...

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

- Wesley Ivan Hurt, Sep 08 2019

MATHEMATICA

Table[Sum[Sum[Sum[(i * Mod[i - 1, 2] + j * Mod[j - 1, 2] + k * Mod[k - 1, 2] + (n - i - j - k) * Mod[n - i - j - k - 1, 2]), {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 80}]

PROG

(PARI) a(n) = sum(k=1, n\4, sum(j=k, (n-k)\3, sum(i=j, (n-j-k)\2, (i * ((i-1) % 2) + j * ((j-1) % 2) + k * ((k-1) % 2) + (n-i-j-k) * ((n-i-j-k-1) % 2))))); \\ Michel Marcus, Sep 08 2019

CROSSREFS

Sequence in context: A064361 A303403 A064407 * A198392 A052289 A309547

Adjacent sequences:  A309516 A309517 A309518 * A309520 A309521 A309522

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Aug 05 2019

EXTENSIONS

Data corrected by Wesley Ivan Hurt, Sep 08 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 4 00:34 EST 2021. Contains 341772 sequences. (Running on oeis4.)