A194525 Second coordinate of (4,7)-Lagrange pair for n.

-1, -2, 1, 0, -1, 2, 1, 0, -1, 2, 1, 0, -1, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 4, 3, 2, 1, 4, 3, 2, 1, 4, 3, 2, 5, 4, 3, 2, 5, 4, 3, 2, 5, 4, 3, 6, 5, 4, 3, 6, 5, 4, 3, 6, 5, 4, 7, 6, 5, 4, 7, 6, 5, 4, 7, 6, 5, 8, 7, 6, 5, 8, 7, 6, 5, 8, 7, 6, 9, 8, 7, 6, 9, 8, 7, 6, 9, 8, 7

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..4.-1..1..3.-2..0..2..4.-1...1...3...5
y(n). -1.-2..1..0.-1..2..1..0.-1..2...1...0..-1
		

Links

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

Crossrefs

Cf. A194508, A194524.

Programs

Mathematica

c = 4; d = 7;
x1 = {2, 4, -1, 1, 3, -2, 0, 2, 4, -1, 1};
y1 = {-1, -2, 1, 0, -1, 2, 1, 0, -1, 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}]  (* A194524 *)
Table[y[n], {n, 1, 100}]  (* A194525 *)
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-11) - a(n-12) for n > 12.

G.f.: x*(-x^10 + 3*x^9 - x^8 - x^7 - x^6 + 3*x^5 - x^4 - x^3 + 3*x^2 - x - 1)/(x^12 - x^11 - x + 1). (End)

a(n) = 3*n - 4*floor((8*n + 6)/11). - Ridouane Oudra, Dec 29 2020