A361471 Size of the symmetric difference of {1,2,3,4}, {2,4,6,8}, ..., {n,2n,3n,4n}.

4, 4, 4, 4, 8, 12, 16, 16, 16, 16, 20, 20, 24, 24, 24, 24, 28, 32, 36, 36, 36, 36, 40, 40, 44, 44, 44, 44, 48, 52, 56, 56, 56, 56, 60, 60, 64, 64, 64, 64, 68, 72, 76, 76, 76, 76, 80, 80, 84, 84, 84, 84, 88, 92, 96, 96, 96, 96, 100, 100, 104, 104, 104, 104, 108

Offset: 1

Author

Guenter Pilz, May 17 2023

Keywords

• nonn
• easy

Links

• P. Y. Huang, W. F. Ke, and G. F. Pilz, The cardinality of some symmetric differences, Proc. Amer. Math. Soc., 138 (2010), 787-797.
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,1,-1).

Crossrefs

Cf. A361458.

Programs

Mathematica

delta[l_, m_] := Complement[Join[l, m], Intersection[l, m]];
Nabl[s_, n_] := (d = {}; Do[d = delta[d, s*j], {j, Range[n]}]; d);
Table[Length[Nabl[Range[1, 4], n]], {n, 100}]

Formula

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