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A194527 Second coordinate of (5,6)-Lagrange pair for n.

%I A194527 #15 Dec 30 2020 03:02:46
%S A194527 1,2,-2,-1,0,1,2,3,-1,0,2,2,3,-1,0,1,2,3,4,0,1,3,3,4,0,1,2,3,4,5,1,2,
%T A194527 4,4,5,1,2,3,4,5,6,2,3,5,5,6,2,3,4,5,6,7,3,4,6,6,7,3,4,5,6,7,8,4,5,7,
%U A194527 7,8,4,5,6,7,8,9,5,6,8,8,9,5,6,7,8,9,10,6,7,9,9,10,6,7,8,9,10,11,7,8,10,10
%N A194527 Second coordinate of (5,6)-Lagrange pair for n.
%C A194527 See A194508.
%H A194527 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,1,-1).
%F A194527 From _Chai Wah Wu_, Jan 21 2020: (Start)
%F A194527 a(n) = a(n-1) + a(n-11) - a(n-12) for n > 12.
%F A194527 G.f.: x*(-x^11 + 2*x^10 + x^9 - 4*x^8 + x^7 + x^6 + x^5 + x^4 + x^3 - 4*x^2 + x + 1)/(x^12 - x^11 - x + 1). (End)
%F A194527 a(n) = n + 1 + floor(2*n/11) - 5*floor((2*n + 5)/11) - floor((2*n + 10)/11). - _Ridouane Oudra_, Dec 29 2020
%e A194527 This table shows (x(n),y(n)) for 1<=n<=13:
%e A194527 n...... 1..2..3..4..5..6..7..8..9..10..11..12..13
%e A194527 x(n).. -1.-2..3..2..1..0.-1.-2..3..2..-1...0..-1
%e A194527 y(n)... 1..2.-2.-1..0..1..2..3.-1..0...2...2...3
%t A194527 c = 5; d = 6;
%t A194527 x1 = {-1, -2, 3, 2, 1, 0, -1, -2, 3, 2, -1}; y1 = {1, 2, -2, -1, 0, 1,
%t A194527    2, 3, -1, 0, 2};
%t A194527 x[n_] := If[n <= c + d, x1[[n]], x[n - c - d] + 1]
%t A194527 y[n_] := If[n <= c + d, y1[[n]], y[n - c - d] + 1]
%t A194527 Table[x[n], {n, 1, 100}]  (* A194526 *)
%t A194527 Table[y[n], {n, 1, 100}]  (* A194527 *)
%t A194527 r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]
%t A194527 TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 30}]]
%Y A194527 Cf. A194508, A194526.
%K A194527 sign
%O A194527 1,2
%A A194527 _Clark Kimberling_, Aug 28 2011