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A194519 Second coordinate of (3,7)-Lagrange pair for n. 4
1, -1, 0, 1, -1, 0, 1, -1, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 5, 3, 4, 5, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 4, 5, 6, 4, 5, 6, 7, 5, 6, 7, 5, 6, 7, 5, 6, 7, 8, 6, 7, 8, 6, 7, 8, 6, 7, 8, 9, 7, 8, 9, 7, 8, 9, 7, 8, 9, 10, 8, 9, 10, 8, 9, 10, 8, 9, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,11

COMMENTS

See A194508.

LINKS

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

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

FORMULA

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

a(n) = a(n-1) + a(n-10) - a(n-11) for n > 11.

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

a(n) = n - 3*floor((3*n+6)/10). - Ridouane Oudra, Sep 06 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).. -2..3..1.-1..4..2..0..5..3..1..-1...4...2

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

MATHEMATICA

c = 3; d = 7;

x1 = {-2, 3, 1, -1, 4, 2, 0, 5, 3, 1}; y1 = {1, -1, 0, 1, -1, 0,

  1, -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}]  (* A194518 *)

Table[y[n], {n, 1, 100}]  (* A194519 *)

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, A194518.

Sequence in context: A025684 A025678 A073189 * A025855 A215590 A097203

Adjacent sequences:  A194516 A194517 A194518 * A194520 A194521 A194522

KEYWORD

sign

AUTHOR

Clark Kimberling, Aug 28 2011

STATUS

approved

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Last modified September 28 02:44 EDT 2020. Contains 337392 sequences. (Running on oeis4.)