

A274615


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


3



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
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OFFSET

0,2


LINKS

Table of n, a(n) for n=0..67.
F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: nonattacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52.


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 = (1t)*(1t^16).  N. J. A. Sloane, Jul 06 2019


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] (* JeanFrançois Alcover, Feb 28 2020, after Alois P. Heinz in A269526 *)


CROSSREFS

Cf. A274528, A269526; equals A274614(n+1)  1.
Sequence in context: A204579 A113095 A157784 * A258895 A156890 A320480
Adjacent sequences: A274612 A274613 A274614 * A274616 A274617 A274618


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Jun 30 2016


EXTENSIONS

More terms from Alois P. Heinz, Jul 01 2016


STATUS

approved



