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A325690 Number of length-3 integer partitions of n whose largest part is not the sum of the other two. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..61.

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

Column k = 3 of A325592.

Cf. A000041, A001399, A005044, A008642, A069905, A266223.

Cf. A325689, A325691, A325694.

Sequence in context: A096441 A100824 A163227 * A238779 A239832 A240010

Adjacent sequences:  A325687 A325688 A325689 * A325691 A325692 A325693

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 15 2019

STATUS

approved

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Last modified June 4 05:19 EDT 2020. Contains 334815 sequences. (Running on oeis4.)