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A194524 First coordinate of (4,7)-Lagrange pair for n. 3
2, 4, -1, 1, 3, -2, 0, 2, 4, -1, 1, 3, 5, 0, 2, 4, -1, 1, 3, 5, 0, 2, 4, 6, 1, 3, 5, 0, 2, 4, 6, 1, 3, 5, 7, 2, 4, 6, 1, 3, 5, 7, 2, 4, 6, 8, 3, 5, 7, 2, 4, 6, 8, 3, 5, 7, 9, 4, 6, 8, 3, 5, 7, 9, 4, 6, 8, 10, 5, 7, 9, 4, 6, 8, 10, 5, 7, 9, 11, 6, 8, 10, 5, 7, 9, 11, 6, 8, 10, 12, 7, 9, 11, 6, 8 (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 (1,0,0,0,0,0,0,0,0,0,1,-1).

FORMULA

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

a(n) = a(n-1) + a(n-11) - a(n-12) for n > 12.

G.f.: x*(2*x^10 - 5*x^9 + 2*x^8 + 2*x^7 + 2*x^6 - 5*x^5 + 2*x^4 + 2*x^3 - 5*x^2 + 2*x + 2)/(x^12 - x^11 - x + 1). (End)

a(n) = 2*n - 7*floor((3*n + 4)/11). - 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).. 2..4.-1..1..3.-2..0..2..4.-1...1...3...5

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

MATHEMATICA

c = 4; d = 7;

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

y1 = {-1, -2, 1, 0, -1, 2, 1, 0, -1, 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}]  (* A194524 *)

Table[y[n], {n, 1, 100}]  (* A194525 *)

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, A194525.

Sequence in context: A158570 A295224 A074749 * A117136 A139227 A269750

Adjacent sequences:  A194521 A194522 A194523 * A194525 A194526 A194527

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.)