A194513 Second coordinate of (2,7)-Lagrange pair for n.

-1, 0, -1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 11, 10, 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, A194512.

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}]]

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

a(n) = n - 2*floor((4*n + 6)/9). - Ridouane Oudra, Dec 28 2020