A194515 Second coordinate of (3,4)-Lagrange pair for n.

1, -1, 0, 1, 2, 0, 1, 2, 0, 1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 2, 3, 4, 2, 3, 4, 5, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 4, 5, 6, 7, 5, 6, 7, 5, 6, 7, 8, 6, 7, 8, 6, 7, 8, 9, 7, 8, 9, 7, 8, 9, 10, 8, 9, 10, 8, 9, 10, 11, 9, 10, 11, 9, 10, 11, 12, 10, 11, 12, 10, 11, 12, 13, 11, 12, 13, 11, 12, 13, 14

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

Links

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

Crossrefs

Cf. A194508, A194514.

Programs

Mathematica

c = 3; d = 4;
x1 = {-1, 2, 1, 0, -1, 2, 1}; y1 = {1, -1, 0, 1, 2, 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}]  (* A194514 *)
Table[y[n], {n, 1, 100}]  (* A194515 *)
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-7) - a(n-8) for n > 8.

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

a(n) = n - 3*floor((2*n + 3)/7). - Ridouane Oudra, Dec 29 2020