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A194529 Second coordinate of (5,8)-Lagrange pair for n.

%I A194529 #12 Dec 29 2020 10:52:04
%S A194529 2,-1,1,-2,0,2,-1,1,3,0,2,4,1,3,0,2,-1,1,3,0,2,4,1,3,5,2,4,1,3,0,2,4,
%T A194529 1,3,5,2,4,6,3,5,2,4,1,3,5,2,4,6,3,5,7,4,6,3,5,2,4,6,3,5,7,4,6,8,5,7,
%U A194529 4,6,3,5,7,4,6,8,5,7,9,6,8,5,7,4,6,8,5,7,9,6,8,10,7,9,6,8,5
%N A194529 Second coordinate of (5,8)-Lagrange pair for n.
%C A194529 See A194508.
%F A194529 From _Chai Wah Wu_, Jan 24 2020: (Start)
%F A194529 a(n) = a(n-1) + a(n-13) - a(n-14) for n > 14.
%F A194529 G.f.: x*(-3*x^12 + 2*x^11 + 2*x^10 - 3*x^9 + 2*x^8 + 2*x^7 - 3*x^6 + 2*x^5 + 2*x^4 - 3*x^3 + 2*x^2 - 3*x + 2)/(x^14 - x^13 - x + 1). (End)
%F A194529 a(n) = 7*n - 5*floor((9*n + 3)/13) - 5*floor((9*n + 8)/13). - _Ridouane Oudra_, Dec 29 2020
%e A194529 This table shows (x(n),y(n)) for 1<=n<=13:
%e A194529 n..... 1..2..3..4..5..6..7..8..9..10..11..12..13
%e A194529 x(n)..-3..2.-1..4..1.-2..3..0.-3..2..-1..-4...1
%e A194529 y(n).. 2.-1..1.-2..0..2.-1..1..3..0...2...4...1
%t A194529 c = 5; d = 8;
%t A194529 x1 = {-3, 2, -1, 4, 1, -2, 3, 0, -3, 2, -1, -4, 1};
%t A194529 y1 = {2, -1, 1, -2, 0, 2, -1, 1, 3, 0, 2, 4, 1};
%t A194529 x[n_] := If[n <= c + d, x1[[n]], x[n - c - d] + 1]
%t A194529 y[n_] := If[n <= c + d, y1[[n]], y[n - c - d] + 1]
%t A194529 Table[x[n], {n, 1, 100}]  (* A194528 *)
%t A194529 Table[y[n], {n, 1, 100}]  (* A194529 *)
%t A194529 r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]
%t A194529 TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 40}]]
%Y A194529 Cf. A194508, A194528.
%K A194529 sign
%O A194529 1,1
%A A194529 _Clark Kimberling_, Aug 28 2011