A194510 First coordinate of (2,5)-Lagrange pair for n.

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

Offset

1,1

Comments

See A194508.

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