A194509 Second coordinate of (2,3)-Lagrange pair for n.

1, 0, 1, 0, 1, 2, 1, 2, 1, 2, 3, 2, 3, 2, 3, 4, 3, 4, 3, 4, 5, 4, 5, 4, 5, 6, 5, 6, 5, 6, 7, 6, 7, 6, 7, 8, 7, 8, 7, 8, 9, 8, 9, 8, 9, 10, 9, 10, 9, 10, 11, 10, 11, 10, 11, 12, 11, 12, 11, 12, 13, 12, 13, 12, 13, 14, 13, 14, 13, 14, 15, 14, 15, 14, 15, 16, 15, 16, 15, 16, 17, 16

Offset: 1

Author

Clark Kimberling, Aug 27 2011

Keywords

• nonn
• easy

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

Links

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

Crossrefs

Cf. A194508.

Programs

Mathematica

c = 2; d = 3;
x1 = {-1, 1, 0, 2, 1}; y1 = {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}] (* A194508 *)
Table[y[n], {n, 1, 100}] (* A194509 *)
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-5) - a(n-6) for n > 6.

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

a(n) = n - 2*floor((2*n + 2)/5). - Ridouane Oudra, Dec 25 2020

a(n) = a(n-1) + (-1)^((n-1) mod 5) for n > 1. - Alexander Van Plantinga, Dec 14 2021