A357849 Number of integer partitions (w,x,y) summing to n such that 2w = 3x + 4y.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3

Offset

0,34

Links

Table of n, a(n) for n=0..86.

Example

The partitions for n = 34, 64, 89, 119, 144:
  (21,10,3)  (39,22,3)  (54,32,3)   (72,44,3)   (87,54,3)
             (40,16,8)  (55,26,8)   (73,38,8)   (88,48,8)
                        (56,20,13)  (74,32,13)  (89,42,13)
                                    (75,26,18)  (90,36,18)
                                                (91,30,23)

Mathematica

Table[Length[Select[IntegerPartitions[n, {3}], 2*#[[1]]==3*#[[2]]+4*#[[3]]&]], {n, 0, 100}]

Prog

(Python)
def A357849(n): return sum(1 for y in range(1, n-1) if (m:=2*n-6*y)>=5*y and 5*(n-y)>=2*m and m%5==0) # Chai Wah Wu, Nov 02 2022

Crossrefs

Partitions are counted by A000041, strict A000009.

The ordered version appears to be A008676, ranked by A357489.

These partitions are ranked by A358102.

Sequence in context: A293451 A063014 A286361 * A097295 A220572 A083896

Adjacent sequences: A357846 A357847 A357848 * A357850 A357851 A357852

Keyword

nonn

Author

Gus Wiseman, Nov 02 2022

Status

approved