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A140102
Term-by-term differences of A140101 and A140100; also, equals the complement of A140103, which is the term-by-term sums of A140101 and A140100, where A140101 is the complement of A140100.
15
0, 1, 2, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 18, 19, 21, 22, 23, 24, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 38, 40, 41, 42, 44, 45, 46, 47, 49, 50, 52, 53, 54, 55, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 70, 71, 72, 73, 75, 76, 78, 79, 80, 81, 83, 84, 85, 87, 88, 89, 90, 92, 93
OFFSET
0,3
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 0..50000, Sep 13 2016 (First 1001 terms from Reinhard Zumkeller)
F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52.
FORMULA
a(n) = A140101(n) - A140100(n).
Theorem: the limit of A140103(n)/A140102(n) = t^2 = 3.38297576...
where the limit of A140101(n)/A140100(n) = t = 1.839286755...
and t = tribonacci constant satisfies: t^3 = 1 + t + t^2.
MAPLE
See link.
MATHEMATICA
nmax = 100; y[0] = 0; x[1] = 1; y[1] = 2; x[n_] := x[n] = For[yn = y[n-1] + 1, True, yn++, For[xn = x[n-1] + 1, xn < yn, xn++, xx = Array[x, n-1]; yy = Array[y, n-1]; If[FreeQ[xx, xn | yn] && FreeQ[yy, xn | yn] && FreeQ[yy - xx, yn - xn] && FreeQ[yy + xx, yn - xn], y[n] = yn; Return[xn]]]];
Do[x[n], {n, 1, nmax}];
Join[{0}, yy - xx] (* Jean-François Alcover, Aug 01 2018 *)
PROG
(PARI) {X=[1]; Y=[2]; D=[1]; S=[3]; print1(Y[1]-X[1]", "); for(n=1, 100, for(j=2, 2*n, if(setsearch(Set(concat(X, Y)), j)==0, Xt=concat(X, j); for(k=j+1, 3*n, if(setsearch(Set(concat(Xt, Y)), k)==0, if(setsearch(Set(concat(D, S)), k-j)==0, if(setsearch(Set(concat(D, S)), k+j)==0, X=Xt; Y=concat(Y, k); D=concat(D, k-j); S=concat(S, k+j); print1(Y[ #X]-X[ #Y]", "); break); break))))))}
CROSSREFS
Cf. A140103 (complement); A140100, A140101; A058265.
For first differences of A140100, A140101, A140102, A140103 see A305392, A305374, A305393, A305394.
Sequence in context: A023733 A154112 A039101 * A376956 A288866 A084437
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 04 2008
EXTENSIONS
Terms computed by Reinhard Zumkeller.
Offset and initial term changed by N. J. A. Sloane, Oct 10 2016
STATUS
approved