A325696 Number of length-3 strict compositions of n such that no part is the sum of the other two.

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.

Links

Table of n, a(n) for n=0..55.

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. A000079, A001399, A005044, A266223.

Cf. A325686, A325688, A325689 (non-strict case), A325695.

Sequence in context: A298026 A315816 A315817 * A337018 A315818 A315819

Adjacent sequences: A325693 A325694 A325695 * A325697 A325698 A325699

Keyword

nonn

Author

Gus Wiseman, May 15 2019

Status

approved