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A194521 Second coordinate of (3,8)-Lagrange pair for n.

%I A194521 #15 Dec 30 2020 03:03:44
%S A194521 -1,1,0,-1,1,0,3,1,0,-1,1,0,2,1,0,2,1,4,2,1,0,2,1,3,2,1,3,2,5,3,2,1,3,
%T A194521 2,4,3,2,4,3,6,4,3,2,4,3,5,4,3,5,4,7,5,4,3,5,4,6,5,4,6,5,8,6,5,4,6,5,
%U A194521 7,6,5,7,6,9,7,6,5,7,6,8,7,6,8,7,10,8,7,6,8,7,9,8,7,9,8,11,9
%N A194521 Second coordinate of (3,8)-Lagrange pair for n.
%C A194521 See A194508.
%H A194521 <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 A194521 From _Chai Wah Wu_, Jan 21 2020: (Start)
%F A194521 a(n) = a(n-1) + a(n-11) - a(n-12) for n > 12.
%F A194521 G.f.: x*(2*x^10 - x^9 - x^8 - 2*x^7 + 3*x^6 - x^5 + 2*x^4 - x^3 - x^2 + 2*x - 1)/(x^12 - x^11 - x + 1). (End)
%F A194521 a(n) = 2*n - 4*floor((7*n + 5)/11) + 4*floor((7*n + 6)/11) - 3*floor((7*n + 7)/11). - _Ridouane Oudra_, Dec 29 2020
%e A194521 This table shows (x(n),y(n)) for 1<=n<=13:
%e A194521 n..... 1..2..3..4..5..6..7..8..9..10..11..12..13
%e A194521 x(n).. 3.-2..1..4.-1..2..5..0..3..4...1...4..-1
%e A194521 y(n). -1..1..0.-1..1..0..3..1..0.-1...1...0...2
%t A194521 c = 3; d = 8;
%t A194521 x1 = {3, -2, 1, 4, -1, 2, 5, 0, 3, 4, 1};
%t A194521 y1 = {-1, 1, 0, -1, 1, 0, 3, 1, 0, -1, 1};
%t A194521 x[n_] := If[n <= c + d, x1[[n]], x[n - c - d] + 1]
%t A194521 y[n_] := If[n <= c + d, y1[[n]], y[n - c - d] + 1]
%t A194521 Table[x[n], {n, 1, 100}]  (* A194520 *)
%t A194521 Table[y[n], {n, 1, 100}]  (* A194521 *)
%t A194521 r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]
%t A194521 TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 30}]]
%Y A194521 Cf. A194508, A194520.
%K A194521 sign
%O A194521 1,7
%A A194521 _Clark Kimberling_, Aug 28 2011