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A309513 Number of even parts in the partitions of n into 3 parts. 0
0, 0, 0, 0, 1, 2, 5, 4, 7, 8, 12, 12, 18, 18, 24, 24, 31, 32, 41, 40, 49, 50, 60, 60, 72, 72, 84, 84, 97, 98, 113, 112, 127, 128, 144, 144, 162, 162, 180, 180, 199, 200, 221, 220, 241, 242, 264, 264, 288, 288, 312, 312, 337, 338, 365, 364, 391, 392, 420, 420 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..59.

Index entries for sequences related to partitions

FORMULA

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

Conjectures from Colin Barker, Aug 06 2019: (Start)

G.f.: x^4*(1 + x + 3*x^2 - x^3 + 2*x^4) / ((1 - x)^3*(1 + x)^2*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)).

a(n) = a(n-1) + a(n-4) - a(n-5) + a(n-6) - a(n-7) - a(n-10) + a(n-11) for n>10.

(End)

EXAMPLE

Figure 1: The partitions of n into 3 parts for n = 3, 4, ...

                                                          1+1+8

                                                   1+1+7  1+2+7

                                                   1+2+6  1+3+6

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

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

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

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

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

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

  n  |     3      4      5      6      7      8      9     10      ...

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

a(n) |     0      1      2      5      4      7      8     12      ...

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

MATHEMATICA

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

CROSSREFS

Sequence in context: A023843 A153990 A154811 * A296203 A036237 A015948

Adjacent sequences:  A309510 A309511 A309512 * A309514 A309515 A309516

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Aug 05 2019

STATUS

approved

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Last modified April 19 13:00 EDT 2021. Contains 343114 sequences. (Running on oeis4.)