A194513 - OEIS

%I #15 Dec 29 2020 02:52:01

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

%C See A194508.

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

%F a(n) = a(n-1) + a(n-9) - a(n-10) for n > 10.

%F 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 a(n) = n - 2*floor((4*n + 6)/9). - _Ridouane Oudra_, Dec 28 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)... 4..1..5..2.-1..3..0..4..1..5...2...6...3

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

%t c = 2; d = 7;

%t x1 = {4, 1, 5, 2, -1, 3, 0, 4, 1}; y1 = {-1, 0, -1, 0, 1, 0, 1, 0, 1};

%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}] (* A194512 *)

%t Table[y[n], {n, 1, 100}] (* A194513 *)

%t Table[y[n], {n, 1, 100}]

%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, A194512.

%K sign

%O 1,14

%A _Clark Kimberling_, Aug 28 2011