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A194514 First coordinate of (3,4)-Lagrange pair for n.

%I A194514 #15 Dec 29 2020 02:51:52
%S A194514 -1,2,1,0,-1,2,1,0,3,2,1,0,3,2,1,4,3,2,1,4,3,2,5,4,3,2,5,4,3,6,5,4,3,
%T A194514 6,5,4,7,6,5,4,7,6,5,8,7,6,5,8,7,6,9,8,7,6,9,8,7,10,9,8,7,10,9,8,11,
%U A194514 10,9,8,11,10,9,12,11,10,9,12,11,10,13,12,11,10,13,12,11,14,13,12,11,14,13
%N A194514 First coordinate of (3,4)-Lagrange pair for n.
%C A194514 See A194508.
%H A194514 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,-1).
%F A194514 From _Chai Wah Wu_, Jan 21 2020: (Start)
%F A194514 a(n) = a(n-1) + a(n-7) - a(n-8) for n > 8.
%F A194514 G.f.: x*(-x^6 + 3*x^5 - x^4 - x^3 - x^2 + 3*x - 1)/(x^8 - x^7 - x + 1). (End)
%F A194514 a(n) = 3*n - 4*floor((5*n + 3)/7). - _Ridouane Oudra_, Dec 28 2020
%e A194514 This table shows (x(n),y(n)) for 1<=n<=13:
%e A194514 n...... 1..2..3..4..5..6..7..8..9..10..11..12..13
%e A194514 x(n)...-1..2..1..0.-1..2..1..0..3..2...1...0...3
%e A194514 y(n)... 1.-1..0..1..2..0..1..2..0..1...2...3...1
%t A194514 c = 3; d = 4;
%t A194514 x1 = {-1, 2, 1, 0, -1, 2, 1}; y1 = {1, -1, 0, 1, 2, 0, 1};
%t A194514 x[n_] := If[n <= c + d, x1[[n]], x[n - c - d] + 1]
%t A194514 y[n_] := If[n <= c + d, y1[[n]], y[n - c - d] + 1]
%t A194514 Table[x[n], {n, 1, 100}]  (* A194514 *)
%t A194514 Table[y[n], {n, 1, 100}]  (* A194515 *)
%t A194514 r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]
%t A194514 TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 30}]]
%Y A194514 Cf. A194508, A194515.
%K A194514 sign
%O A194514 1,2
%A A194514 _Clark Kimberling_, Aug 28 2011