A194517 Second coordinate of (3,5)-Lagrange pair for n.

-1, 1, 0, -1, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 4, 3, 2, 4, 3, 2, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 7, 6, 5, 7, 6, 5, 7, 6, 8, 7, 6, 8, 7, 6, 8, 7, 9, 8, 7, 9, 8, 7, 9, 8, 10, 9, 8, 10, 9, 8, 10, 9, 11, 10, 9, 11, 10, 9, 11, 10, 12, 11, 10, 12, 11, 10, 12, 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)... 2.-1..1..3..0..2.-1..1..3..0...2...4...1
y(n).. -1..1..0.-1..1..0..2..1..0..2...1...0...2
		

Links

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

Crossrefs

Cf. A194508, A194517.

Programs

Mathematica

c = 3; d = 5;
x1 = {2, -1, 1, 3, 0, 2, -1, 1}; y1 = {-1, 1, 0, -1, 1, 0, 2, 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}]  (* A194516 *)
Table[y[n], {n, 1, 100}]  (* A194517 *)
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}]]

Formula

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

a(n) = a(n-1) + a(n-8) - a(n-9) for n > 9.

G.f.: -x*(x^3 + x - 1)*(x^4 - 2*x^3 + x - 1)/(x^9 - x^8 - x + 1). (End)

a(n) = 2*n - 3*floor((5*n + 4)/8). - Ridouane Oudra, Dec 29 2020