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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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.
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
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 *)
CROSSREFS
Cf. A274528, A269526; equals A274614(n+1) - 1.
Sequence in context: A204579 A113095 A157784 * A258895 A156890 A320480
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 30 2016
EXTENSIONS
More terms from Alois P. Heinz, Jul 01 2016
STATUS
approved

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Last modified June 24 00:53 EDT 2024. Contains 373661 sequences. (Running on oeis4.)