login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A309512 Sum of the odd parts in the partitions of n into 3 parts. 0
0, 0, 0, 3, 2, 6, 6, 18, 18, 37, 34, 64, 64, 100, 100, 161, 156, 220, 220, 310, 310, 417, 410, 542, 542, 686, 686, 877, 868, 1064, 1064, 1304, 1304, 1571, 1560, 1866, 1866, 2190, 2190, 2583, 2570, 2970, 2970, 3432, 3432, 3931, 3916, 4468, 4468, 5044, 5044 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..50.

Index entries for sequences related to partitions

FORMULA

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

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

G.f.: x^3*(3 - x + 7*x^2 - x^3 + 13*x^4 + x^5 + 18*x^6 + 19*x^8 - x^9 + 9*x^10 + x^11 + 3*x^12 + x^13) / ((1 - x)^4*(1 + x)^3*(1 - x + x^2)^2*(1 + x^2)^2*(1 + x + x^2)^2).

a(n) = a(n-1) - a(n-2) + a(n-3) + a(n-4) - a(n-5) + 3*a(n-6) - 3*a(n-7) + 2*a(n-8) - 2*a(n-9) - 2*a(n-10) + 2*a(n-11) - 3*a(n-12) + 3*a(n-13) - a(n-14) + a(n-15) + a(n-16) - a(n-17) + a(n-18) - a(n-19) for n>18.

(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) |     3      2      6      6     18     18     37     34      ...

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

MATHEMATICA

Table[Sum[Sum[i*Mod[i, 2] + j*Mod[j, 2] + (n - i - j)*Mod[n - i - j, 2], {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 0, 100}]

CROSSREFS

Sequence in context: A014686 A053090 A264400 * A225367 A283479 A087237

Adjacent sequences:  A309509 A309510 A309511 * A309513 A309514 A309515

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Aug 05 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 November 19 08:44 EST 2019. Contains 329318 sequences. (Running on oeis4.)