A194527 Second coordinate of (5,6)-Lagrange pair for n.
1, 2, -2, -1, 0, 1, 2, 3, -1, 0, 2, 2, 3, -1, 0, 1, 2, 3, 4, 0, 1, 3, 3, 4, 0, 1, 2, 3, 4, 5, 1, 2, 4, 4, 5, 1, 2, 3, 4, 5, 6, 2, 3, 5, 5, 6, 2, 3, 4, 5, 6, 7, 3, 4, 6, 6, 7, 3, 4, 5, 6, 7, 8, 4, 5, 7, 7, 8, 4, 5, 6, 7, 8, 9, 5, 6, 8, 8, 9, 5, 6, 7, 8, 9, 10, 6, 7, 9, 9, 10, 6, 7, 8, 9, 10, 11, 7, 8, 10, 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).. -1.-2..3..2..1..0.-1.-2..3..2..-1...0..-1 y(n)... 1..2.-2.-1..0..1..2..3.-1..0...2...2...3
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 = 5; d = 6; x1 = {-1, -2, 3, 2, 1, 0, -1, -2, 3, 2, -1}; y1 = {1, 2, -2, -1, 0, 1, 2, 3, -1, 0, 2}; 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}] (* A194526 *) Table[y[n], {n, 1, 100}] (* A194527 *) 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*(-x^11 + 2*x^10 + x^9 - 4*x^8 + x^7 + x^6 + x^5 + x^4 + x^3 - 4*x^2 + x + 1)/(x^12 - x^11 - x + 1). (End)
a(n) = n + 1 + floor(2*n/11) - 5*floor((2*n + 5)/11) - floor((2*n + 10)/11). - Ridouane Oudra, Dec 29 2020
Comments