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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
OFFSET
1,1
COMMENTS
See A194508.
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
Sequence in context: A158570 A295224 A074749 * A117136 A362142 A139227
KEYWORD
sign
AUTHOR
Clark Kimberling, Aug 28 2011
STATUS
approved