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A194526 First coordinate of (5,6)-Lagrange pair for n. 3
-1, -2, 3, 2, 1, 0, -1, -2, 3, 2, -1, 0, -1, 4, 3, 2, 1, 0, -1, 4, 3, 0, 1, 0, 5, 4, 3, 2, 1, 0, 5, 4, 1, 2, 1, 6, 5, 4, 3, 2, 1, 6, 5, 2, 3, 2, 7, 6, 5, 4, 3, 2, 7, 6, 3, 4, 3, 8, 7, 6, 5, 4, 3, 8, 7, 4, 5, 4, 9, 8, 7, 6, 5, 4, 9, 8, 5, 6, 5, 10, 9, 8, 7, 6, 5, 10, 9, 6, 7, 6, 11, 10, 9, 8, 7, 6 (list; graph; refs; listen; history; text; internal format)
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 (1,0,0,0,0,0,0,0,0,0,1,-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*(2*x^11 - 3*x^10 - x^9 + 5*x^8 - x^7 - x^6 - x^5 - x^4 - x^3 + 5*x^2 - x - 1)/(x^12 - x^11 - x + 1). (End)

a(n) = 5*n - 2 - 2*floor(9*n/11) - 6*floor((9*n + 5)/11) + 2*floor((9*n + 10)/11). - Ridouane Oudra, Dec 30 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, A194527.

Sequence in context: A037891 A037899 A037837 * A165033 A179766 A081134

Adjacent sequences:  A194523 A194524 A194525 * A194527 A194528 A194529

KEYWORD

sign

AUTHOR

Clark Kimberling, Aug 28 2011

STATUS

approved

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Last modified April 11 15:49 EDT 2021. Contains 342886 sequences. (Running on oeis4.)