A194528 First coordinate of (5,8)-Lagrange pair for n.

-3, 2, -1, 4, 1, -2, 3, 0, -3, 2, -1, -4, 1, -2, 3, 0, 5, 2, -1, 4, 1, -2, 3, 0, -3, 2, -1, 4, 1, 6, 3, 0, 5, 2, -1, 4, 1, -2, 3, 0, 5, 2, 7, 4, 1, 6, 3, 0, 5, 2, -1, 4, 1, 6, 3, 8, 5, 2, 7, 4, 1, 6, 3, 0, 5, 2, 7, 4, 9, 6, 3, 8, 5, 2, 7, 4, 1, 6, 3, 8, 5, 10, 7, 4, 9, 6, 3, 8, 5, 2

Offset

1,1

Comments

See A194508.

Links

Table of n, a(n) for n=1..90.

Formula

From Chai Wah Wu, Jan 24 2020: (Start)

a(n) = a(n-1) + a(n-13) - a(n-14) for n > 14.

G.f.: x*(5*x^12 - 3*x^11 - 3*x^10 + 5*x^9 - 3*x^8 - 3*x^7 + 5*x^6 - 3*x^5 - 3*x^4 + 5*x^3 - 3*x^2 + 5*x - 3)/(x^14 - x^13 - x + 1). (End)

a(n) = 5*n - 8*floor((4*n + 4)/13) - 8*floor((4*n + 9)/13). - 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)..-3..2.-1..4..1.-2..3..0.-3..2..-1..-4...1
y(n).. 2.-1..1.-2..0..2.-1..1..3..0...2...4...1

Mathematica

c = 5; d = 8;
x1 = {-3, 2, -1, 4, 1, -2, 3, 0, -3, 2, -1, -4, 1};
y1 = {2, -1, 1, -2, 0, 2, -1, 1, 3, 0, 2, 4, 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}]  (* A194528 *)
Table[y[n], {n, 1, 100}]  (* A194529 *)
r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]
TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 40}]]

Crossrefs

Cf. A194508, A194529.

Sequence in context: A270828 A325315 A230845 * A194520 A082727 A264597

Adjacent sequences: A194525 A194526 A194527 * A194529 A194530 A194531

Keyword

sign

Author

Clark Kimberling, Aug 28 2011

Status

approved