A325695 Number of length-3 strict integer partitions of n such that the largest part is not the sum of the other two.

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

Offset

0,10

Links

Table of n, a(n) for n=0..62.

Formula

Conjectures from Colin Barker, May 15 2019: (Start)

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)

a(n) = A325696(n)/6. - Alois P. Heinz, Jun 18 2020

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

Cf. A000041, A001399, A005044, A008642, A069905, A124278.

Cf. A325686, A325690, A325691, A325694, A325696.

Sequence in context: A115207 A093048 A141732 * A186545 A008623 A035546

Adjacent sequences: A325692 A325693 A325694 * A325696 A325697 A325698

Keyword

nonn

Author

Gus Wiseman, May 15 2019

Status

approved