login
A325690
Number of length-3 integer partitions of n whose largest part is not the sum of the other two.
8
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
0,6
COMMENTS
Confirmed recurrence relation from Colin Barker for n <= 10000. - Fausto A. C. Cariboni, Feb 19 2022
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..10000
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)
EXAMPLE
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)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n, {3}], #[[1]]!=#[[2]]+#[[3]]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 15 2019
STATUS
approved