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A194513 Second coordinate of (2,7)-Lagrange pair for n.

%I A194513 #15 Dec 29 2020 02:52:01
%S A194513 -1,0,-1,0,1,0,1,0,1,0,1,0,1,2,1,2,1,2,1,2,1,2,3,2,3,2,3,2,3,2,3,4,3,
%T A194513 4,3,4,3,4,3,4,5,4,5,4,5,4,5,4,5,6,5,6,5,6,5,6,5,6,7,6,7,6,7,6,7,6,7,
%U A194513 8,7,8,7,8,7,8,7,8,9,8,9,8,9,8,9,8,9,10,9,10,9,10,9,10,9,10,11,10,11
%N A194513 Second coordinate of (2,7)-Lagrange pair for n.
%C A194513 See A194508.
%H A194513 <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 A194513 From _Chai Wah Wu_, Jan 21 2020: (Start)
%F A194513 a(n) = a(n-1) + a(n-9) - a(n-10) for n > 10.
%F A194513 G.f.: x*(x^8 - x^7 + x^6 - x^5 + x^4 + x^3 - x^2 + x - 1)/(x^10 - x^9 - x + 1). (End)
%F A194513 a(n) = n - 2*floor((4*n + 6)/9). - _Ridouane Oudra_, Dec 28 2020
%e A194513 This table shows (x(n),y(n)) for 1<=n<=13:
%e A194513 n...... 1..2..3..4..5..6..7..8..9..10..11..12..13
%e A194513 x(n)... 4..1..5..2.-1..3..0..4..1..5...2...6...3
%e A194513 y(n).. -1..0.-1..0..1..0..1..0..1..0...1...0...1
%t A194513 c = 2; d = 7;
%t A194513 x1 = {4, 1, 5, 2, -1, 3, 0, 4, 1}; y1 = {-1, 0, -1, 0, 1, 0, 1, 0, 1};
%t A194513 x[n_] := If[n <= c + d, x1[[n]], x[n - c - d] + 1]
%t A194513 y[n_] := If[n <= c + d, y1[[n]], y[n - c - d] + 1]
%t A194513 Table[x[n], {n, 1, 100}] (* A194512 *)
%t A194513 Table[y[n], {n, 1, 100}] (* A194513 *)
%t A194513 Table[y[n], {n, 1, 100}]
%t A194513 r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]
%t A194513 TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 30}]]
%Y A194513 Cf. A194508, A194512.
%K A194513 sign
%O A194513 1,14
%A A194513 _Clark Kimberling_, Aug 28 2011