A194516 First coordinate of (3,5)-Lagrange pair for n.
2, -1, 1, 3, 0, 2, -1, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 5, 2, 4, 1, 3, 5, 2, 4, 6, 3, 5, 2, 4, 6, 3, 5, 7, 4, 6, 3, 5, 7, 4, 6, 8, 5, 7, 4, 6, 8, 5, 7, 9, 6, 8, 5, 7, 9, 6, 8, 10, 7, 9, 6, 8, 10, 7, 9, 11, 8, 10, 7, 9, 11, 8, 10, 12, 9, 11, 8, 10, 12, 9, 11, 13, 10, 12, 9, 11, 13, 10, 12, 14, 11, 13, 10
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)... 2.-1..1..3..0..2.-1..1..3..0...2...4...1 y(n).. -1..1..0.-1..1..0..2..1..0..2...1...0...2
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,1,-1).
Programs
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Mathematica
c = 3; d = 5; x1 = {2, -1, 1, 3, 0, 2, -1, 1}; y1 = {-1, 1, 0, -1, 1, 0, 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}] (* A194516 *) Table[y[n], {n, 1, 100}] (* A194517 *) 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}]] LinearRecurrence[{1,0,0,0,0,0,0,1,-1},{2,-1,1,3,0,2,-1,1,3},100] (* Harvey P. Dale, Nov 29 2024 *)
Formula
From Chai Wah Wu, Jan 21 2020: (Start)
a(n) = a(n-1) + a(n-8) - a(n-9) for n > 9.
G.f.: x*(2*x^7 - 3*x^6 + 2*x^5 - 3*x^4 + 2*x^3 + 2*x^2 - 3*x + 2)/(x^9 - x^8 - x + 1). (End)
a(n) = 2*n - 5*floor((3*n + 3)/8). - Ridouane Oudra, Dec 29 2020
Comments