A194518 First coordinate of (3,7)-Lagrange pair for n.

-2, 3, 1, -1, 4, 2, 0, 5, 3, 1, -1, 4, 2, 0, 5, 3, 1, 6, 4, 2, 0, 5, 3, 1, 6, 4, 2, 7, 5, 3, 1, 6, 4, 2, 7, 5, 3, 8, 6, 4, 2, 7, 5, 3, 8, 6, 4, 9, 7, 5, 3, 8, 6, 4, 9, 7, 5, 10, 8, 6, 4, 9, 7, 5, 10, 8, 6, 11, 9, 7, 5, 10, 8, 6, 11, 9, 7, 12, 10, 8, 6, 11, 9, 7, 12, 10, 8, 13, 11, 9, 7, 12, 10

Offset: 1

Author

Clark Kimberling, Aug 28 2011

Keywords

• sign

Comments

See A194508.

Examples

			This table shows (x(n),y(n)) for 1<=n<=13:
n...... 1..2..3..4..5..6..7..8..9..10..11..12..13
x(n).. -2..3..1.-1..4..2..0..5..3..1..-1...4...2
y(n)... 1.-1..0..1.-1..0..1.-1..0..1...2...0...1
		

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,1,-1).

Crossrefs

Cf. A194508, A194519.

Programs

Mathematica

c = 3; d = 7;
x1 = {-2, 3, 1, -1, 4, 2, 0, 5, 3, 1}; y1 = {1, -1, 0, 1, -1, 0,
  1, -1, 0, 1};
x[n_] := If[n <= c + d, x1[[n]], x[n - c - d] + 1]
y[n_] := If[n <= c + d, y1[[n]], y[n - c - d] + 1]
Table[x[n], {n, 1, 100}]  (* A194518 *)
Table[y[n], {n, 1, 100}]  (* A194519 *)
r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]
TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 30}]]
LinearRecurrence[{1,0,0,0,0,0,0,0,0,1,-1},{-2,3,1,-1,4,2,0,5,3,1,-1},100] (* Harvey P. Dale, Sep 02 2023 *)

Formula

From Chai Wah Wu, Jan 21 2020: (Start)

a(n) = a(n-1) + a(n-10) - a(n-11) for n > 11.

G.f.: x*(-2*x^9 - 2*x^8 + 5*x^7 - 2*x^6 - 2*x^5 + 5*x^4 - 2*x^3 - 2*x^2 + 5*x - 2)/(x^11 - x^10 - x + 1). (End)

a(n) = 5*n - 7*floor((7*n+3)/10). - Ridouane Oudra, Sep 06 2020