A194520 First coordinate of (3,8)-Lagrange pair for n.
3, -2, 1, 4, -1, 2, 5, 0, 3, 4, 1, 4, -1, 2, 5, 0, 3, 6, 1, 4, 5, 2, 5, 0, 3, 6, 1, 4, 7, 2, 5, 6, 3, 6, 1, 4, 7, 2, 5, 8, 3, 6, 7, 4, 7, 2, 5, 8, 3, 6, 9, 4, 7, 8, 5, 8, 3, 6, 9, 4, 7, 10, 5, 8, 9, 6, 9, 4, 7, 10, 5, 8, 11, 6, 9, 10, 7, 10, 5, 8, 11, 6, 9, 12, 7, 10, 11, 8, 11, 6, 9
Offset: 1
Keywords
Examples
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..5..0..3..4...1...4..-1 y(n). -1..1..0.-1..1..0..3..1..0.-1...1...0...2
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,1,-1).
Programs
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Mathematica
c = 3; d = 8; x1 = {3, -2, 1, 4, -1, 2, 5, 0, 3, 4, 1}; y1 = {-1, 1, 0, -1, 1, 0, 3, 1, 0, -1, 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}] (* A194520 *) Table[y[n], {n, 1, 100}] (* A194521 *) 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}]]
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*(-3*x^10 + x^9 + 3*x^8 - 5*x^7 + 3*x^6 + 3*x^5 - 5*x^4 + 3*x^3 + 3*x^2 - 5*x + 3)/(x^12 - x^11 - x + 1). (End)
a(n) = 3*n - 6*floor((4*n + 3)/11) - 2*floor((4*n + 4)/11). - Ridouane Oudra, Dec 29 2020
Comments