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A361472
Size of the symmetric differences of {1,2,3,4,5}, {2,4,6,8,10}, ..., {n,2n,3n,4n,5n}.
1
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
1,1
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, 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).
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
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}]
CROSSREFS
Sequence in context: A367150 A368121 A368126 * A346172 A114547 A217293
KEYWORD
nonn,easy
AUTHOR
Guenter Pilz, May 17 2023
STATUS
approved