A194529 Second coordinate of (5,8)-Lagrange pair for n.

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

Offset

1,1

Comments

See A194508.

Links

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

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

a(n) = 7*n - 5*floor((9*n + 3)/13) - 5*floor((9*n + 8)/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, A194528.

Sequence in context: A306660 A357332 A347367 * A055138 A177717 A155997

Adjacent sequences: A194526 A194527 A194528 * A194530 A194531 A194532

Keyword

sign

Author

Clark Kimberling, Aug 28 2011

Status

approved