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A194522 First coordinate of (4,5)-Lagrange pair for n.

%I A194522 #15 Dec 29 2020 10:21:14
%S A194522 -1,-2,2,1,0,-1,3,2,1,0,-1,3,2,1,0,4,3,2,1,0,4,3,2,1,5,4,3,2,1,5,4,3,
%T A194522 2,6,5,4,3,2,6,5,4,3,7,6,5,4,3,7,6,5,4,8,7,6,5,4,8,7,6,5,9,8,7,6,5,9,
%U A194522 8,7,6,10,9,8,7,6,10,9,8,7,11,10,9,8,7,11,10,9,8,12,11,10,9,8,12,11,10,9
%N A194522 First coordinate of (4,5)-Lagrange pair for n.
%C A194522 See A194508.
%H A194522 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,1,-1).
%F A194522 From _Chai Wah Wu_, Jan 21 2020: (Start)
%F A194522 a(n) = a(n-1) + a(n-9) - a(n-10) for n > 10.
%F A194522 G.f.: x*(-x^8 - x^7 + 4*x^6 - x^5 - x^4 - x^3 + 4*x^2 - x - 1)/(x^10 - x^9 - x + 1). (End)
%F A194522 a(n) = 4*n - 5*floor((7*n + 4)/9). - _Ridouane Oudra_, Dec 29 2020
%e A194522 This table shows (x(n),y(n)) for 1<=n<=13:
%e A194522 n...... 1..2..3..4..5..6..7..8..9..10..11..12..13
%e A194522 x(n).. -1.-2..2..1..0.-1..3..2..1..0..-1...3...2
%e A194522 y(n)... 1..2..1..0..1..2.-1..0..1..2...3...2...1
%t A194522 Remove["Global`*"];
%t A194522 c = 4; d = 5;
%t A194522 x1 = {-1, -2, 2, 1, 0, -1, 3, 2, 1}; y1 = {1, 2, 1, 0, 1, 2, -1, 0, 1};
%t A194522 x[n_] := If[n <= c + d, x1[[n]], x[n - c - d] + 1]
%t A194522 y[n_] := If[n <= c + d, y1[[n]], y[n - c - d] + 1]
%t A194522 Table[x[n], {n, 1, 100}]  (* A194522 *)
%t A194522 Table[y[n], {n, 1, 100}]  (* A194523 *)
%t A194522 r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]
%t A194522 TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 30}]]
%Y A194522 Cf. A194508, A194523.
%K A194522 sign
%O A194522 1,2
%A A194522 _Clark Kimberling_, Aug 28 2011