A194527 - OEIS

%I #15 Dec 30 2020 03:02:46

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

%C See A194508.

%H <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 From _Chai Wah Wu_, Jan 21 2020: (Start)

%F a(n) = a(n-1) + a(n-11) - a(n-12) for n > 12.

%F 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 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 This table shows (x(n),y(n)) for 1<=n<=13:

%e n...... 1..2..3..4..5..6..7..8..9..10..11..12..13

%e x(n).. -1.-2..3..2..1..0.-1.-2..3..2..-1...0..-1

%e y(n)... 1..2.-2.-1..0..1..2..3.-1..0...2...2...3

%t c = 5; d = 6;

%t x1 = {-1, -2, 3, 2, 1, 0, -1, -2, 3, 2, -1}; y1 = {1, 2, -2, -1, 0, 1,

%t    2, 3, -1, 0, 2};

%t x[n_] := If[n <= c + d, x1[[n]], x[n - c - d] + 1]

%t y[n_] := If[n <= c + d, y1[[n]], y[n - c - d] + 1]

%t Table[x[n], {n, 1, 100}]  (* A194526 *)

%t Table[y[n], {n, 1, 100}]  (* A194527 *)

%t r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]

%t TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 30}]]

%Y Cf. A194508, A194526.

%K sign

%O 1,2

%A _Clark Kimberling_, Aug 28 2011