A361458 Size of the symmetric difference of {1,2,3}, {2,4,6}, ..., {n,2n,3n}.

3, 4, 3, 4, 7, 8, 11, 12, 11, 12, 15, 16, 19, 20, 19, 20, 23, 24, 27, 28, 27, 28, 31, 32, 35, 36, 35, 36, 39, 40, 43, 44, 43, 44, 47, 48, 51, 52, 51, 52, 55, 56, 59, 60, 59, 60, 63, 64, 67, 68, 67, 68, 71, 72, 75, 76, 75, 76, 79, 80, 83, 84, 83, 84, 87, 88, 91

Offset

1,1

Comments

a(n) is also the terms of (x+x^2+x^3) + (x^2+x^4+x^6) + ... + (x^n+x^2n+x^3n) in GF(2)[x].

Links

Table of n, a(n) for n=1..67.

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 (1,0,0,0,0,1,-1).

Formula

G.f.: x*(x^5+3*x^4+x^3-x^2+x+3)/(x^7-x^6-x+1). - Alois P. Heinz, May 17 2023

6*a(n) = 1 -(-1)^n +8*n +8*A103368(n-1). - R. J. Mathar, Jan 11 2024

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, 3], n]], {n, 100}]

Prog

(PARI) a(n) = {my(m=0); for(k = 0, n-1, m = bitxor(m, 2^k+2^(2*k+1)+2^(3*k+2))); hammingweight(m)} \\ Thomas Scheuerle, May 17 2023

Crossrefs

Cf. A361471.

Sequence in context: A135800 A178152 A006984 * A087275 A265305 A072942

Adjacent sequences: A361455 A361456 A361457 * A361459 A361460 A361461

Keyword

nonn,easy

Author

Guenter Pilz, May 17 2023

Status

approved