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A194524 First coordinate of (4,7)-Lagrange pair for n.

%I A194524 #16 Dec 29 2020 10:21:23
%S A194524 2,4,-1,1,3,-2,0,2,4,-1,1,3,5,0,2,4,-1,1,3,5,0,2,4,6,1,3,5,0,2,4,6,1,
%T A194524 3,5,7,2,4,6,1,3,5,7,2,4,6,8,3,5,7,2,4,6,8,3,5,7,9,4,6,8,3,5,7,9,4,6,
%U A194524 8,10,5,7,9,4,6,8,10,5,7,9,11,6,8,10,5,7,9,11,6,8,10,12,7,9,11,6,8
%N A194524 First coordinate of (4,7)-Lagrange pair for n.
%C A194524 See A194508.
%H A194524 <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 A194524 From _Chai Wah Wu_, Jan 21 2020: (Start)
%F A194524 a(n) = a(n-1) + a(n-11) - a(n-12) for n > 12.
%F A194524 G.f.: x*(2*x^10 - 5*x^9 + 2*x^8 + 2*x^7 + 2*x^6 - 5*x^5 + 2*x^4 + 2*x^3 - 5*x^2 + 2*x + 2)/(x^12 - x^11 - x + 1). (End)
%F A194524 a(n) = 2*n - 7*floor((3*n + 4)/11). - _Ridouane Oudra_, Dec 29 2020
%e A194524 This table shows (x(n),y(n)) for 1<=n<=13:
%e A194524 n..... 1..2..3..4..5..6..7..8..9..10..11..12..13
%e A194524 x(n).. 2..4.-1..1..3.-2..0..2..4.-1...1...3...5
%e A194524 y(n). -1.-2..1..0.-1..2..1..0.-1..2...1...0..-1
%t A194524 c = 4; d = 7;
%t A194524 x1 = {2, 4, -1, 1, 3, -2, 0, 2, 4, -1, 1};
%t A194524 y1 = {-1, -2, 1, 0, -1, 2, 1, 0, -1, 2, 1};
%t A194524 x[n_] := If[n <= c + d, x1[[n]], x[n - c - d] + 1]
%t A194524 y[n_] := If[n <= c + d, y1[[n]], y[n - c - d] + 1]
%t A194524 Table[x[n], {n, 1, 100}]  (* A194524 *)
%t A194524 Table[y[n], {n, 1, 100}]  (* A194525 *)
%t A194524 r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]
%t A194524 TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 30}]]
%Y A194524 Cf. A194508, A194525.
%K A194524 sign
%O A194524 1,1
%A A194524 _Clark Kimberling_, Aug 28 2011