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A194517 Second coordinate of (3,5)-Lagrange pair for n.

%I A194517 #15 Dec 29 2020 09:33:23
%S A194517 -1,1,0,-1,1,0,2,1,0,2,1,0,2,1,3,2,1,3,2,1,3,2,4,3,2,4,3,2,4,3,5,4,3,
%T A194517 5,4,3,5,4,6,5,4,6,5,4,6,5,7,6,5,7,6,5,7,6,8,7,6,8,7,6,8,7,9,8,7,9,8,
%U A194517 7,9,8,10,9,8,10,9,8,10,9,11,10,9,11,10,9,11,10,12,11,10,12,11,10,12,11
%N A194517 Second coordinate of (3,5)-Lagrange pair for n.
%C A194517 See A194508.
%H A194517 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,1,-1).
%F A194517 From _Chai Wah Wu_, Jan 21 2020: (Start)
%F A194517 a(n) = a(n-1) + a(n-8) - a(n-9) for n > 9.
%F A194517 G.f.: -x*(x^3 + x - 1)*(x^4 - 2*x^3 + x - 1)/(x^9 - x^8 - x + 1). (End)
%F A194517 a(n) = 2*n - 3*floor((5*n + 4)/8). - _Ridouane Oudra_, Dec 29 2020
%e A194517 This table shows (x(n),y(n)) for 1<=n<=13:
%e A194517 n...... 1..2..3..4..5..6..7..8..9..10..11..12..13
%e A194517 x(n)... 2.-1..1..3..0..2.-1..1..3..0...2...4...1
%e A194517 y(n).. -1..1..0.-1..1..0..2..1..0..2...1...0...2
%t A194517 c = 3; d = 5;
%t A194517 x1 = {2, -1, 1, 3, 0, 2, -1, 1}; y1 = {-1, 1, 0, -1, 1, 0, 2, 1};
%t A194517 x[n_] := If[n <= c + d, x1[[n]], x[n - c - d] + 1]
%t A194517 y[n_] := If[n <= c + d, y1[[n]], y[n - c - d] + 1]
%t A194517 Table[x[n], {n, 1, 100}]  (* A194516 *)
%t A194517 Table[y[n], {n, 1, 100}]  (* A194517 *)
%t A194517 r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]
%t A194517 TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 30}]]
%Y A194517 Cf. A194508, A194517.
%K A194517 sign
%O A194517 1,7
%A A194517 _Clark Kimberling_, Aug 28 2011