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A194520 First coordinate of (3,8)-Lagrange pair for n.

%I A194520 #15 Dec 29 2020 10:50:47
%S A194520 3,-2,1,4,-1,2,5,0,3,4,1,4,-1,2,5,0,3,6,1,4,5,2,5,0,3,6,1,4,7,2,5,6,3,
%T A194520 6,1,4,7,2,5,8,3,6,7,4,7,2,5,8,3,6,9,4,7,8,5,8,3,6,9,4,7,10,5,8,9,6,9,
%U A194520 4,7,10,5,8,11,6,9,10,7,10,5,8,11,6,9,12,7,10,11,8,11,6,9
%N A194520 First coordinate of (3,8)-Lagrange pair for n.
%C A194520 See A194508.
%H A194520 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,1,-1).
%F A194520 From _Chai Wah Wu_, Jan 21 2020: (Start)
%F A194520 a(n) = a(n-1) + a(n-11) - a(n-12) for n > 12.
%F A194520 G.f.: x*(-3*x^10 + x^9 + 3*x^8 - 5*x^7 + 3*x^6 + 3*x^5 - 5*x^4 + 3*x^3 + 3*x^2 - 5*x + 3)/(x^12 - x^11 - x + 1). (End)
%F A194520 a(n) = 3*n - 6*floor((4*n + 3)/11) - 2*floor((4*n + 4)/11). - _Ridouane Oudra_, Dec 29 2020
%e A194520 This table shows (x(n),y(n)) for 1<=n<=13:
%e A194520 n..... 1..2..3..4..5..6..7..8..9..10..11..12..13
%e A194520 x(n).. 3.-2..1..4.-1..2..5..0..3..4...1...4..-1
%e A194520 y(n). -1..1..0.-1..1..0..3..1..0.-1...1...0...2
%t A194520 c = 3; d = 8;
%t A194520 x1 = {3, -2, 1, 4, -1, 2, 5, 0, 3, 4, 1};
%t A194520 y1 = {-1, 1, 0, -1, 1, 0, 3, 1, 0, -1, 1};
%t A194520 x[n_] := If[n <= c + d, x1[[n]], x[n - c - d] + 1]
%t A194520 y[n_] := If[n <= c + d, y1[[n]], y[n - c - d] + 1]
%t A194520 Table[x[n], {n, 1, 100}]  (* A194520 *)
%t A194520 Table[y[n], {n, 1, 100}]  (* A194521 *)
%t A194520 r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]
%t A194520 TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 30}]]
%Y A194520 Cf. A194508, A194521.
%K A194520 sign
%O A194520 1,1
%A A194520 _Clark Kimberling_, Aug 28 2011