A194510 - OEIS

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A194510

First coordinate of (2,5)-Lagrange pair for n.

3

3, 1, -1, 2, 0, 3, 1, 4, 2, 0, 3, 1, 4, 2, 5, 3, 1, 4, 2, 5, 3, 6, 4, 2, 5, 3, 6, 4, 7, 5, 3, 6, 4, 7, 5, 8, 6, 4, 7, 5, 8, 6, 9, 7, 5, 8, 6, 9, 7, 10, 8, 6, 9, 7, 10, 8, 11, 9, 7, 10, 8, 11, 9, 12, 10, 8, 11, 9, 12, 10, 13, 11, 9, 12, 10, 13, 11, 14, 12, 10, 13, 11, 14, 12, 15, 13, 11, 14

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

LINKS

Table of n, a(n) for n=1..88.

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

a(n) = 3*n - 5*floor((4*n + 2)/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, A194511.

Sequence in context: A016467 A342275 A324049 * A331311 A285770 A370892

Adjacent sequences: A194507 A194508 A194509 * A194511 A194512 A194513

KEYWORD

sign

AUTHOR

Clark Kimberling, Aug 27 2011

STATUS

approved