A325690 Number of length-3 integer partitions of n whose largest part is not the sum of the other two.
0, 0, 0, 1, 0, 2, 2, 4, 3, 7, 6, 10, 9, 14, 13, 19, 17, 24, 23, 30, 28, 37, 35, 44, 42, 52, 50, 61, 58, 70, 68, 80, 77, 91, 88, 102, 99, 114, 111, 127, 123, 140, 137, 154, 150, 169, 165, 184, 180, 200, 196, 217, 212, 234, 230, 252, 247, 271, 266, 290, 285, 310
Offset: 0
Keywords
Examples
The a(3) = 1 through a(13) = 14 partitions (A = 10, B = 11):
(111) (221) (222) (322) (332) (333) (433) (443) (444) (544)
(311) (411) (331) (521) (432) (442) (533) (543) (553)
(421) (611) (441) (622) (542) (552) (643)
(511) (522) (631) (551) (732) (652)
(531) (721) (632) (741) (661)
(621) (811) (641) (822) (733)
(711) (722) (831) (742)
(731) (921) (751)
(821) (A11) (832)
(911) (841)
(922)
(931)
(A21)
(B11)
Links
- Fausto A. C. Cariboni, Table of n, a(n) for n = 0..10000
Crossrefs
Programs
-
Mathematica
Table[Length[Select[IntegerPartitions[n,{3}],#[[1]]!=#[[2]]+#[[3]]&]],{n,0,30}]
Formula
Conjectures from Colin Barker, May 15 2019: (Start)
G.f.: x^3*(1 + x^2 + x^3 + x^4) / ((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>8.
(End)
Comments