A194509 Second coordinate of (2,3)-Lagrange pair for n.

1, 0, 1, 0, 1, 2, 1, 2, 1, 2, 3, 2, 3, 2, 3, 4, 3, 4, 3, 4, 5, 4, 5, 4, 5, 6, 5, 6, 5, 6, 7, 6, 7, 6, 7, 8, 7, 8, 7, 8, 9, 8, 9, 8, 9, 10, 9, 10, 9, 10, 11, 10, 11, 10, 11, 12, 11, 12, 11, 12, 13, 12, 13, 12, 13, 14, 13, 14, 13, 14, 15, 14, 15, 14, 15, 16, 15, 16, 15, 16, 17, 16

Offset

1,6

Comments

See A194508.

Links

Table of n, a(n) for n=1..82.

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

Formula

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

a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6.

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

a(n) = n - 2*floor((2*n + 2)/5). - Ridouane Oudra, Dec 25 2020

a(n) = a(n-1) + (-1)^((n-1) mod 5) for n > 1. - Alexander Van Plantinga, Dec 14 2021

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..1..0..2..1..0..2..1..3..2...1...3...2
y(n)... 1..0..1..0..1..2..1..2..1..2...3...2...3

Mathematica

c = 2; d = 3;
x1 = {-1, 1, 0, 2, 1}; y1 = {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}] (* A194508 *)
Table[y[n], {n, 1, 100}] (* A194509 *)
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.

Sequence in context: A265745 A092243 A257564 * A054716 A261641 A325622

Adjacent sequences: A194506 A194507 A194508 * A194510 A194511 A194512

Keyword

nonn,easy

Author

Clark Kimberling, Aug 27 2011

Status

approved