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A194528 First coordinate of (5,8)-Lagrange pair for n.

%I A194528 #12 Dec 29 2020 10:53:16
%S A194528 -3,2,-1,4,1,-2,3,0,-3,2,-1,-4,1,-2,3,0,5,2,-1,4,1,-2,3,0,-3,2,-1,4,1,
%T A194528 6,3,0,5,2,-1,4,1,-2,3,0,5,2,7,4,1,6,3,0,5,2,-1,4,1,6,3,8,5,2,7,4,1,6,
%U A194528 3,0,5,2,7,4,9,6,3,8,5,2,7,4,1,6,3,8,5,10,7,4,9,6,3,8,5,2
%N A194528 First coordinate of (5,8)-Lagrange pair for n.
%C A194528 See A194508.
%F A194528 From _Chai Wah Wu_, Jan 24 2020: (Start)
%F A194528 a(n) = a(n-1) + a(n-13) - a(n-14) for n > 14.
%F A194528 G.f.: x*(5*x^12 - 3*x^11 - 3*x^10 + 5*x^9 - 3*x^8 - 3*x^7 + 5*x^6 - 3*x^5 - 3*x^4 + 5*x^3 - 3*x^2 + 5*x - 3)/(x^14 - x^13 - x + 1). (End)
%F A194528 a(n) = 5*n - 8*floor((4*n + 4)/13) - 8*floor((4*n + 9)/13). - _Ridouane Oudra_, Dec 29 2020
%e A194528 This table shows (x(n),y(n)) for 1<=n<=13:
%e A194528 n..... 1..2..3..4..5..6..7..8..9..10..11..12..13
%e A194528 x(n)..-3..2.-1..4..1.-2..3..0.-3..2..-1..-4...1
%e A194528 y(n).. 2.-1..1.-2..0..2.-1..1..3..0...2...4...1
%t A194528 c = 5; d = 8;
%t A194528 x1 = {-3, 2, -1, 4, 1, -2, 3, 0, -3, 2, -1, -4, 1};
%t A194528 y1 = {2, -1, 1, -2, 0, 2, -1, 1, 3, 0, 2, 4, 1};
%t A194528 x[n_] := If[n <= c + d, x1[[n]], x[n - c - d] + 1]
%t A194528 y[n_] := If[n <= c + d, y1[[n]], y[n - c - d] + 1]
%t A194528 Table[x[n], {n, 1, 100}]  (* A194528 *)
%t A194528 Table[y[n], {n, 1, 100}]  (* A194529 *)
%t A194528 r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]
%t A194528 TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 40}]]
%Y A194528 Cf. A194508, A194529.
%K A194528 sign
%O A194528 1,1
%A A194528 _Clark Kimberling_, Aug 28 2011