A361472 Size of the symmetric differences of {1,2,3,4,5}, {2,4,6,8,10}, ..., {n,2n,3n,4n,5n}.

5, 6, 7, 8, 5, 10, 15, 16, 17, 18, 23, 24, 29, 30, 31, 32, 37, 42, 47, 48, 49, 50, 55, 56, 53, 54, 55, 56, 61, 58, 63, 64, 65, 66, 63, 64, 69, 70, 71, 72, 77, 82, 87, 88, 89, 90, 95, 96, 101, 102, 103, 104, 109, 114, 111, 112, 113, 114, 119, 120, 125, 126, 127

Offset: 1

Author

Guenter Pilz, May 17 2023

Keywords

• nonn
• easy

Links

• Ray Chandler, Table of n, a(n) for n = 1..1000
• 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Crossrefs

Cf. A361458, A361471.

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, 5], n]], {n, 100}]

Formula

G.f.: x*(x^59 +5*x^58 +x^57 +x^56 +x^55 -3*x^54 +5*x^53 +5*x^52 +x^51 +x^50 +x^49 +5*x^48 +x^47 +5*x^46 +x^45 +x^44 +x^43 +5*x^42 +5*x^41 +5*x^40 +x^39 +x^38 +x^37 +5*x^36 +x^35 -3*x^34 +x^33 +x^32 +x^31 +5*x^30 -3*x^29 +5*x^28 +x^27 +x^26 +x^25 -3*x^24 +x^23 +5*x^22 +x^21 +x^20 +x^19 +5*x^18 +5*x^17 +5*x^16 +x^15 +x^14 +x^13 +5*x^12 +x^11 +5*x^10 +x^9 +x^8 +x^7 +5*x^6 +5*x^5 -3*x^4 +x^3 +x^2 +x +5) / (x^61 -x^60 -x +1). - Alois P. Heinz, May 17 2023