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A194519 Second coordinate of (3,7)-Lagrange pair for n.

%I A194519 #15 Sep 06 2020 10:54:51
%S A194519 1,-1,0,1,-1,0,1,-1,0,1,2,0,1,2,0,1,2,0,1,2,3,1,2,3,1,2,3,1,2,3,4,2,3,
%T A194519 4,2,3,4,2,3,4,5,3,4,5,3,4,5,3,4,5,6,4,5,6,4,5,6,4,5,6,7,5,6,7,5,6,7,
%U A194519 5,6,7,8,6,7,8,6,7,8,6,7,8,9,7,8,9,7,8,9,7,8,9,10,8,9,10,8,9,10,8,9,10
%N A194519 Second coordinate of (3,7)-Lagrange pair for n.
%C A194519 See A194508.
%H A194519 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,1,-1).
%F A194519 From _Chai Wah Wu_, Jan 21 2020: (Start)
%F A194519 a(n) = a(n-1) + a(n-10) - a(n-11) for n > 11.
%F A194519 G.f.: x*(x^9 + x^8 - 2*x^7 + x^6 + x^5 - 2*x^4 + x^3 + x^2 - 2*x + 1)/(x^11 - x^10 - x + 1). (End)
%F A194519 a(n) = n - 3*floor((3*n+6)/10). - _Ridouane Oudra_, Sep 06 2020
%e A194519 This table shows (x(n),y(n)) for 1<=n<=13:
%e A194519 n...... 1..2..3..4..5..6..7..8..9..10..11..12..13
%e A194519 x(n).. -2..3..1.-1..4..2..0..5..3..1..-1...4...2
%e A194519 y(n)... 1.-1..0..1.-1..0..1.-1..0..1...2...0...1
%t A194519 c = 3; d = 7;
%t A194519 x1 = {-2, 3, 1, -1, 4, 2, 0, 5, 3, 1}; y1 = {1, -1, 0, 1, -1, 0,
%t A194519   1, -1, 0, 1};
%t A194519 x[n_] := If[n <= c + d, x1[[n]], x[n - c - d] + 1]
%t A194519 y[n_] := If[n <= c + d, y1[[n]], y[n - c - d] + 1]
%t A194519 Table[x[n], {n, 1, 100}]  (* A194518 *)
%t A194519 Table[y[n], {n, 1, 100}]  (* A194519 *)
%t A194519 r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]
%t A194519 TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 30}]]
%Y A194519 Cf. A194508, A194518.
%K A194519 sign
%O A194519 1,11
%A A194519 _Clark Kimberling_, Aug 28 2011