A194511 Second coordinate of (2,5)-Lagrange pair for n.

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

Offset: 1

Author

Clark Kimberling, Aug 27 2011

Keywords

• sign
• 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)... 3..1.-1..2..0..3..1..4..2..0...3...1...4
y(n).. -1..0..1..0..1..0..1..0..1..2...1...2...1
		

Links

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

Crossrefs

Cf. A194508, A194510.

Programs

Mathematica

c = 2; d = 5;
x1 = {3, 1, -1, 2, 0, 3, 1}; y1 = {-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}] (* A194510 *)
Table[y[n], {n, 1, 100}] (* A194511 *)
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 - x^5 + x^4 - x^3 + x^2 + x - 1)/(x^8 - x^7 - x + 1). (End)

a(n) = n - 2*floor((3*n + 4)/7). - Ridouane Oudra, Dec 25 2020

G.f.: x*(1-x^2+x^3)*(x^3+x-1)/((1-x)^2*(1+x+x^2+x^3+x^4+x^5+x^6)). - R. J. Mathar, Feb 04 2022