A194527 Second coordinate of (5,6)-Lagrange pair for n.

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

Offset

1,2

Comments

See A194508.

Links

Table of n, a(n) for n=1..100.

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

a(n) = n + 1 + floor(2*n/11) - 5*floor((2*n + 5)/11) - floor((2*n + 10)/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).. -1.-2..3..2..1..0.-1.-2..3..2..-1...0..-1
y(n)... 1..2.-2.-1..0..1..2..3.-1..0...2...2...3

Mathematica

c = 5; d = 6;
x1 = {-1, -2, 3, 2, 1, 0, -1, -2, 3, 2, -1}; y1 = {1, 2, -2, -1, 0, 1,
   2, 3, -1, 0, 2};
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}]  (* A194526 *)
Table[y[n], {n, 1, 100}]  (* A194527 *)
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, A194526.

Sequence in context: A357701 A307011 A285007 * A104244 A116403 A123149

Adjacent sequences: A194524 A194525 A194526 * A194528 A194529 A194530

Keyword

sign

Author

Clark Kimberling, Aug 28 2011

Status

approved