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

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, 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, 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

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)... 4..1..5..2.-1..3..0..4..1..5...2...6...3
y(n).. -1..0.-1..0..1..0..1..0..1..0...1...0...1
		

Links

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

Crossrefs

Cf. A194508, A194513.

Programs

Mathematica

c = 2; d = 7;
x1 = {4, 1, 5, 2, -1, 3, 0, 4, 1}; y1 = {-1, 0, -1, 0, 1, 0, 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}] (* A194512 *)
Table[y[n], {n, 1, 100}] (* A194513 *)
Table[y[n], {n, 1, 100}]
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[{1,0,0,0,0,0,0,0,1,-1},{4,1,5,2,-1,3,0,4,1,5},100] (* Harvey P. Dale, Dec 27 2023 *)

Formula

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

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

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)

a(n) = 4*n - 7*floor((5*n + 2)/9). - Ridouane Oudra, Dec 28 2020