A194520 First coordinate of (3,8)-Lagrange pair for n.

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

Offset

1,1

Comments

See A194508.

Links

Table of n, a(n) for n=1..91.

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

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

a(n) = 3*n - 6*floor((4*n + 3)/11) - 2*floor((4*n + 4)/11). - Ridouane Oudra, Dec 29 2020

Example

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

Mathematica

c = 3; d = 8;
x1 = {3, -2, 1, 4, -1, 2, 5, 0, 3, 4, 1};
y1 = {-1, 1, 0, -1, 1, 0, 3, 1, 0, -1, 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}]  (* A194520 *)
Table[y[n], {n, 1, 100}]  (* A194521 *)
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}]]

Crossrefs

Cf. A194508, A194521.

Sequence in context: A325315 A230845 A194528 * A082727 A264597 A112603

Adjacent sequences: A194517 A194518 A194519 * A194521 A194522 A194523

Keyword

sign

Author

Clark Kimberling, Aug 28 2011

Status

approved