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A194522 First coordinate of (4,5)-Lagrange pair for n. 3
-1, -2, 2, 1, 0, -1, 3, 2, 1, 0, -1, 3, 2, 1, 0, 4, 3, 2, 1, 0, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 6, 5, 4, 3, 2, 6, 5, 4, 3, 7, 6, 5, 4, 3, 7, 6, 5, 4, 8, 7, 6, 5, 4, 8, 7, 6, 5, 9, 8, 7, 6, 5, 9, 8, 7, 6, 10, 9, 8, 7, 6, 10, 9, 8, 7, 11, 10, 9, 8, 7, 11, 10, 9, 8, 12, 11, 10, 9, 8, 12, 11, 10, 9 (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 (1,0,0,0,0,0,0,0,1,-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 + 4*x^6 - x^5 - x^4 - x^3 + 4*x^2 - x - 1)/(x^10 - x^9 - x + 1). (End)

a(n) = 4*n - 5*floor((7*n + 4)/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, A194523.

Sequence in context: A037890 A037898 A037836 * A165013 A055290 A125629

Adjacent sequences:  A194519 A194520 A194521 * A194523 A194524 A194525

KEYWORD

sign

AUTHOR

Clark Kimberling, Aug 28 2011

STATUS

approved

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Last modified April 14 22:47 EDT 2021. Contains 342971 sequences. (Running on oeis4.)