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A194512 First coordinate of (2,7)-Lagrange pair for n.

%I A194512 #17 Dec 27 2023 15:24:39
%S A194512 4,1,5,2,-1,3,0,4,1,5,2,6,3,0,4,1,5,2,6,3,7,4,1,5,2,6,3,7,4,8,5,2,6,3,
%T A194512 7,4,8,5,9,6,3,7,4,8,5,9,6,10,7,4,8,5,9,6,10,7,11,8,5,9,6,10,7,11,8,
%U A194512 12,9,6,10,7,11,8,12,9,13,10,7,11,8,12,9,13,10,14,11,8,12,9,13,10,14,11
%N A194512 First coordinate of (2,7)-Lagrange pair for n.
%C A194512 See A194508.
%H A194512 <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 A194512 From _Chai Wah Wu_, Jan 21 2020: (Start)
%F A194512 a(n) = a(n-1) + a(n-9) - a(n-10) for n > 10.
%F A194512 G.f.: x*(-3*x^8 + 4*x^7 - 3*x^6 + 4*x^5 - 3*x^4 - 3*x^3 + 4*x^2 - 3*x + 4)/(x^10 - x^9 - x + 1). (End)
%F A194512 a(n) = 4*n - 7*floor((5*n + 2)/9). - _Ridouane Oudra_, Dec 28 2020
%e A194512 This table shows (x(n),y(n)) for 1<=n<=13:
%e A194512 n...... 1..2..3..4..5..6..7..8..9..10..11..12..13
%e A194512 x(n)... 4..1..5..2.-1..3..0..4..1..5...2...6...3
%e A194512 y(n).. -1..0.-1..0..1..0..1..0..1..0...1...0...1
%t A194512 c = 2; d = 7;
%t A194512 x1 = {4, 1, 5, 2, -1, 3, 0, 4, 1}; y1 = {-1, 0, -1, 0, 1, 0, 1, 0, 1};
%t A194512 x[n_] := If[n <= c + d, x1[[n]], x[n - c - d] + 1]
%t A194512 y[n_] := If[n <= c + d, y1[[n]], y[n - c - d] + 1]
%t A194512 Table[x[n], {n, 1, 100}] (* A194512 *)
%t A194512 Table[y[n], {n, 1, 100}] (* A194513 *)
%t A194512 Table[y[n], {n, 1, 100}]
%t A194512 r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]
%t A194512 TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 30}]]
%t A194512 LinearRecurrence[{1,0,0,0,0,0,0,0,1,-1},{4,1,5,2,-1,3,0,4,1,5},100] (* _Harvey P. Dale_, Dec 27 2023 *)
%Y A194512 Cf. A194508, A194513.
%K A194512 sign
%O A194512 1,1
%A A194512 _Clark Kimberling_, Aug 28 2011