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A194516 First coordinate of (3,5)-Lagrange pair for n. 3
2, -1, 1, 3, 0, 2, -1, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 5, 2, 4, 1, 3, 5, 2, 4, 6, 3, 5, 2, 4, 6, 3, 5, 7, 4, 6, 3, 5, 7, 4, 6, 8, 5, 7, 4, 6, 8, 5, 7, 9, 6, 8, 5, 7, 9, 6, 8, 10, 7, 9, 6, 8, 10, 7, 9, 11, 8, 10, 7, 9, 11, 8, 10, 12, 9, 11, 8, 10, 12, 9, 11, 13, 10, 12, 9, 11, 13, 10, 12, 14, 11, 13, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A194508.

LINKS

Table of n, a(n) for n=1..95.

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

FORMULA

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

a(n) = a(n-1) + a(n-8) - a(n-9) for n > 9.

G.f.: x*(2*x^7 - 3*x^6 + 2*x^5 - 3*x^4 + 2*x^3 + 2*x^2 - 3*x + 2)/(x^9 - x^8 - 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)... 2.-1..1..3..0..2.-1..1..3..0...2...4...1

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

MATHEMATICA

c = 3; d = 5;

x1 = {2, -1, 1, 3, 0, 2, -1, 1}; y1 = {-1, 1, 0, -1, 1, 0, 2, 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}]  (* A194516 *)

Table[y[n], {n, 1, 100}]  (* A194517 *)

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, A194517.

Sequence in context: A325687 A230079 A105400 * A299235 A245840 A033774

Adjacent sequences:  A194513 A194514 A194515 * A194517 A194518 A194519

KEYWORD

sign

AUTHOR

Clark Kimberling, Aug 28 2011

STATUS

approved

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Last modified August 12 04:39 EDT 2020. Contains 336436 sequences. (Running on oeis4.)