A274615 Third column (that is, the c=2 column) of array in A274528.

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, 29, 26, 27, 25, 33, 30, 31, 36, 37, 34, 32, 40, 35, 38, 39, 44, 45, 42, 43, 41, 49, 46, 47, 52, 53, 50, 48, 56, 51, 54, 55, 60, 61, 58, 59, 57, 65, 62, 63, 68, 69, 66

Offset: 0

Author

N. J. A. Sloane, Jun 30 2016

Keywords

• nonn

Links

• 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.

Crossrefs

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

Programs

Mathematica

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]];
a[n_] := A[n + 1, 3];
a /@ Range[0, 100] (* Jean-François Alcover, Feb 28 2020, after Alois P. Heinz in A269526 *)

Formula

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

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.

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

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

Extensions

More terms from Alois P. Heinz, Jul 01 2016