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A194511 Second coordinate of (2,5)-Lagrange pair for n. 3
-1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 3, 2, 3, 2, 3, 4, 3, 4, 3, 4, 3, 4, 5, 4, 5, 4, 5, 4, 5, 6, 5, 6, 5, 6, 5, 6, 7, 6, 7, 6, 7, 6, 7, 8, 7, 8, 7, 8, 7, 8, 9, 8, 9, 8, 9, 8, 9, 10, 9, 10, 9, 10, 9, 10, 11, 10, 11, 10, 11, 10, 11, 12, 11, 12, 11, 12, 11, 12, 13, 12, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

See A194508.

LINKS

Table of n, a(n) for n=1..89.

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

FORMULA

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

a(n) = a(n-1) + a(n-7) - a(n-8) for n > 8.

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

a(n) = n - 2*floor((3*n + 4)/7). - Ridouane Oudra, Dec 25 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)... 3..1.-1..2..0..3..1..4..2..0...3...1...4

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

MATHEMATICA

c = 2; d = 5;

x1 = {3, 1, -1, 2, 0, 3, 1}; y1 = {-1, 0, 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}] (* A194510 *)

Table[y[n], {n, 1, 100}] (* A194511 *)

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, A194510.

Sequence in context: A206826 A175835 A123738 * A214526 A245038 A161312

Adjacent sequences:  A194508 A194509 A194510 * A194512 A194513 A194514

KEYWORD

sign

AUTHOR

Clark Kimberling, Aug 27 2011

STATUS

approved

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Last modified April 14 22:45 EDT 2021. Contains 342967 sequences. (Running on oeis4.)