login
Size of the symmetric difference of {1,2,3,4}, {2,4,6,8}, ..., {n,2n,3n,4n}.
2

%I #20 May 18 2023 01:56:21

%S 4,4,4,4,8,12,16,16,16,16,20,20,24,24,24,24,28,32,36,36,36,36,40,40,

%T 44,44,44,44,48,52,56,56,56,56,60,60,64,64,64,64,68,72,76,76,76,76,80,

%U 80,84,84,84,84,88,92,96,96,96,96,100,100,104,104,104,104,108

%N Size of the symmetric difference of {1,2,3,4}, {2,4,6,8}, ..., {n,2n,3n,4n}.

%H P. Y. Huang, W. F. Ke, and G. F. Pilz, <a href="https://doi.org/10.1090/S0002-9939-09-10189-2">The cardinality of some symmetric differences</a>, Proc. Amer. Math. Soc., 138 (2010), 787-797.

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,1,-1).

%F G.f.: 4*x*(x^10+x^6+x^5+x^4+1)/(x^13-x^12-x+1). - _Alois P. Heinz_, May 17 2023

%t delta[l_, m_] := Complement[Join[l, m], Intersection[l, m]];

%t Nabl[s_, n_] := (d = {}; Do[d = delta[d, s*j], {j, Range[n]}]; d);

%t Table[Length[Nabl[Range[1, 4], n]], {n, 100}]

%Y Cf. A361458.

%K nonn,easy

%O 1,1

%A _Guenter Pilz_, May 17 2023