A194523 Second coordinate of (4,5)-Lagrange pair for n.

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

Offset

1,2

Comments

See A194508.

Links

Table of n, a(n) for n=1..96.

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

Formula

From Chai Wah Wu, Jan 21 2020: (Start)

a(n) = a(n-1) + a(n-9) - a(n-10) for n > 10.

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

a(n) = n - 4*floor((n + 2)/9) - 2*floor((n + 5)/9) - 2*floor((n + 6)/9). - 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).. -1.-2..2..1..0.-1..3..2..1..0..-1...3...2
y(n)... 1..2..1..0..1..2.-1..0..1..2...3...2...1

Mathematica

Remove["Global`*"];
c = 4; d = 5;
x1 = {-1, -2, 2, 1, 0, -1, 3, 2, 1}; y1 = {1, 2, 1, 0, 1, 2, -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}]  (* A194522 *)
Table[y[n], {n, 1, 100}]  (* A194523 *)
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, A194522.

Sequence in context: A282938 A065368 A010751 * A362721 A180714 A170959

Adjacent sequences: A194520 A194521 A194522 * A194524 A194525 A194526

Keyword

sign

Author

Clark Kimberling, Aug 28 2011

Status

approved