A274615 - OEIS

%I #31 Mar 07 2020 13:52:25

%S 1,4,5,2,0,8,3,6,7,12,13,10,11,9,17,14,15,20,21,18,16,24,19,22,23,28,

%T 29,26,27,25,33,30,31,36,37,34,32,40,35,38,39,44,45,42,43,41,49,46,47,

%U 52,53,50,48,56,51,54,55,60,61,58,59,57,65,62,63,68,69,66

%N Third column (that is, the c=2 column) of array in A274528.

%H F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, <a href="https://www.combinatorics.org/ojs/index.php/eljc/article/view/v27i1p52/8039">Queens in exile: non-attacking queens on infinite chess boards</a>, Electronic J. Combin., 27:1 (2020), #P1.52.

%F This is a permutation of the nonnegative numbers (see the general proof in A269526).

%F It appears that the permutation is given by a(0)=0, and, for n >= 1, n = 16t+i (0 <= i <= 15) we have a(16t+i) = 16t + c_i, where [c_0, ..., c_15] = [-1,4,5,2,0,8,3,6,7,12,13,10,11,9,17,14]. - _N. J. A. Sloane_, Jul 01 2016, based on an email from _Bob Selcoe_, Jun 29 2016.

%F Equivalently, it appears that this sequence has g.f. = f/g where

%F f = 2*t^17 - 3*t^15 + 8*t^14 - 2*t^13 + t^12 - 3*t^11 + t^10 + 5*t^9 + t^8 + 3*t^7 - 5*t^6 + 8*t^5 - 2*t^4 - 3*t^3 + t^2 + 3*t + 1, and g = (1-t)*(1-t^16). - _N. J. A. Sloane_, Jul 06 2019

%t A[n_, k_] := A[n, k] = Module[{m, s}, If[n == 1 && k == 1, 0, s = Join[ Table[A[i, k], {i, 1, n - 1}], Table[A[n, j], {j, 1, k - 1}], Table[A[n - t, k - t], {t, 1, Min[n, k] - 1}], Table[A[n + j, k - j], {j, 1, k - 1}]]; For[m = 0, MemberQ[s, m], m++]; m]];

%t a[n_] := A[n + 1, 3];

%t a /@ Range[0, 100] (* _Jean-François Alcover_, Feb 28 2020, after _Alois P. Heinz_ in A269526 *)

%Y Cf. A274528, A269526; equals A274614(n+1) - 1.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jun 30 2016

%E More terms from _Alois P. Heinz_, Jul 01 2016