VOOZH about

URL: https://oeis.org/A325696

⇱ A325696 - OEIS

login
A325696
Number of length-3 strict compositions of n such that no part is the sum of the other two.
1
0, 0, 0, 0, 0, 0, 0, 6, 6, 18, 12, 30, 30, 48, 42, 72, 66, 96, 90, 126, 120, 162, 150, 198, 192, 240, 228, 288, 276, 336, 324, 390, 378, 450, 432, 510, 498, 576, 558, 648, 630, 720, 702, 798, 780, 882, 858, 966, 948, 1056, 1032, 1152, 1128, 1248, 1224, 1350
OFFSET
0,8
COMMENTS
A composition of n is a finite sequence of positive integers summing to n. It is strict if all parts are distinct.
FORMULA
Conjectures from Colin Barker, May 16 2019: (Start)
G.f.: 6*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) = 6 * A325695(n). - Alois P. Heinz, Jun 18 2020
EXAMPLE
The a(6) = 6 through a(10) = 12 compositions:
(124) (125) (126) (127)
(142) (152) (135) (136)
(214) (215) (153) (163)
(241) (251) (162) (172)
(412) (512) (216) (217)
(421) (521) (234) (271)
(243) (316)
(261) (361)
(315) (613)
(324) (631)
(342) (712)
(351) (721)
(423)
(432)
(513)
(531)
(612)
(621)
MATHEMATICA
Table[Length[Cases[Join@@Permutations/@IntegerPartitions[n, {3}], {x_, y_, z_}/; x!=y!=z&&x+y!=z&&x!=y+z&&y!=x+z]], {n, 0, 30}]
CROSSREFS
Cf. A325686, A325688, A325689 (non-strict case), A325695.
Sequence in context: A298026 A315816 A315817 * A337018 A315818 A315819
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 15 2019
STATUS
approved