|
|
A325695
|
|
Number of length-3 strict integer partitions of n such that the largest part is not the sum of the other two.
|
|
4
|
|
|
0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 5, 5, 8, 7, 12, 11, 16, 15, 21, 20, 27, 25, 33, 32, 40, 38, 48, 46, 56, 54, 65, 63, 75, 72, 85, 83, 96, 93, 108, 105, 120, 117, 133, 130, 147, 143, 161, 158, 176, 172, 192, 188, 208, 204, 225, 221, 243, 238, 261, 257, 280, 275
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,10
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x^7*(1 + x + 2*x^2) / ((1 - x)^3*(1 + x)^2*(1 + x^2)*(1 + x + x^2)).
a(n) = a(n-2) + a(n-3) + a(n-4) - a(n-5) - a(n-6) - a(n-7) + a(n-9) for n>9.
(End)
|
|
EXAMPLE
|
The a(7) = 1 through a(15) = 12 partitions (A = 10, B = 11, C = 12):
(421) (521) (432) (631) (542) (543) (643) (653) (654)
(531) (721) (632) (732) (652) (842) (753)
(621) (641) (741) (742) (851) (762)
(731) (831) (751) (932) (843)
(821) (921) (832) (941) (852)
(841) (A31) (861)
(931) (B21) (942)
(A21) (951)
(A32)
(A41)
(B31)
(C21)
|
|
MATHEMATICA
|
Table[Length[Select[IntegerPartitions[n, {3}], UnsameQ@@#&&#[[1]]!=#[[2]]+#[[3]]&]], {n, 0, 30}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|