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

Author

Gus Wiseman, Nov 02 2022

Keywords

• nonn

Examples

			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)
		

Crossrefs

Partitions are counted by A000041, strict A000009.

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

These partitions are ranked by A358102.

Programs

Mathematica

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

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