%I #20 May 21 2023 20:18:58

%S 5,6,7,8,5,10,15,16,17,18,23,24,29,30,31,32,37,42,47,48,49,50,55,56,

%T 53,54,55,56,61,58,63,64,65,66,63,64,69,70,71,72,77,82,87,88,89,90,95,

%U 96,101,102,103,104,109,114,111,112,113,114,119,120,125,126,127

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

%H Ray Chandler, <a href="/A361472/b361472.txt">Table of n, a(n) for n = 1..1000</a>

%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_61">Index entries for linear recurrences with constant coefficients</a>, 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).

%F 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

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

%Y Cf. A361458, A361471.

%K nonn,easy

%O 1,1

%A _Guenter Pilz_, May 17 2023