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A194514 First coordinate of (3,4)-Lagrange pair for n. 3
-1, 2, 1, 0, -1, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 4, 3, 2, 1, 4, 3, 2, 5, 4, 3, 2, 5, 4, 3, 6, 5, 4, 3, 6, 5, 4, 7, 6, 5, 4, 7, 6, 5, 8, 7, 6, 5, 8, 7, 6, 9, 8, 7, 6, 9, 8, 7, 10, 9, 8, 7, 10, 9, 8, 11, 10, 9, 8, 11, 10, 9, 12, 11, 10, 9, 12, 11, 10, 13, 12, 11, 10, 13, 12, 11, 14, 13, 12, 11, 14, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A194508.

LINKS

Table of n, a(n) for n=1..91.

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

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..1..0.-1..2..1..0..3..2...1...0...3

y(n)... 1.-1..0..1..2..0..1..2..0..1...2...3...1

MATHEMATICA

c = 3; d = 4;

x1 = {-1, 2, 1, 0, -1, 2, 1}; y1 = {1, -1, 0, 1, 2, 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}]  (* A194514 *)

Table[y[n], {n, 1, 100}]  (* A194515 *)

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, A194515.

Sequence in context: A268834 A285914 A096875 * A324667 A258260 A094713

Adjacent sequences:  A194511 A194512 A194513 * A194515 A194516 A194517

KEYWORD

sign

AUTHOR

Clark Kimberling, Aug 28 2011

STATUS

approved

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Last modified September 28 02:07 EDT 2020. Contains 337392 sequences. (Running on oeis4.)