cp's OEIS Frontend

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

%I A325696 #11 Jun 18 2020 19:38:36
%S A325696 0,0,0,0,0,0,0,6,6,18,12,30,30,48,42,72,66,96,90,126,120,162,150,198,
%T A325696 192,240,228,288,276,336,324,390,378,450,432,510,498,576,558,648,630,
%U A325696 720,702,798,780,882,858,966,948,1056,1032,1152,1128,1248,1224,1350
%N A325696 Number of length-3 strict compositions of n such that no part is the sum of the other two.
%C A325696 A composition of n is a finite sequence of positive integers summing to n. It is strict if all parts are distinct.
%F A325696 Conjectures from _Colin Barker_, May 16 2019: (Start)
%F A325696 G.f.: 6*x^7*(1 + x + 2*x^2) / ((1 - x)^3*(1 + x)^2*(1 + x^2)*(1 + x + x^2)).
%F A325696 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.
%F A325696 (End)
%F A325696 a(n) = 6 * A325695(n). - _Alois P. Heinz_, Jun 18 2020
%e A325696 The a(6) = 6 through a(10) = 12 compositions:
%e A325696   (124)  (125)  (126)  (127)
%e A325696   (142)  (152)  (135)  (136)
%e A325696   (214)  (215)  (153)  (163)
%e A325696   (241)  (251)  (162)  (172)
%e A325696   (412)  (512)  (216)  (217)
%e A325696   (421)  (521)  (234)  (271)
%e A325696                 (243)  (316)
%e A325696                 (261)  (361)
%e A325696                 (315)  (613)
%e A325696                 (324)  (631)
%e A325696                 (342)  (712)
%e A325696                 (351)  (721)
%e A325696                 (423)
%e A325696                 (432)
%e A325696                 (513)
%e A325696                 (531)
%e A325696                 (612)
%e A325696                 (621)
%t A325696 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}]
%Y A325696 Cf. A000079, A001399, A005044, A266223.
%Y A325696 Cf. A325686, A325688, A325689 (non-strict case), A325695.
%K A325696 nonn
%O A325696 0,8
%A A325696 _Gus Wiseman_, May 15 2019