A194523 Second coordinate of (4,5)-Lagrange pair for n.
1, 2, 1, 0, 1, 2, -1, 0, 1, 2, 3, 2, 1, 2, 3, 0, 1, 2, 3, 4, 3, 2, 3, 4, 1, 2, 3, 4, 5, 4, 3, 4, 5, 2, 3, 4, 5, 6, 5, 4, 5, 6, 3, 4, 5, 6, 7, 6, 5, 6, 7, 4, 5, 6, 7, 8, 7, 6, 7, 8, 5, 6, 7, 8, 9, 8, 7, 8, 9, 6, 7, 8, 9, 10, 9, 8, 9, 10, 7, 8, 9, 10, 11, 10, 9, 10, 11, 8, 9, 10, 11, 12, 11, 10, 11, 12
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..2..1..0.-1..3..2..1..0..-1...3...2 y(n)... 1..2..1..0..1..2.-1..0..1..2...3...2...1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,1,-1).
Programs
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Mathematica
Remove["Global`*"]; c = 4; d = 5; x1 = {-1, -2, 2, 1, 0, -1, 3, 2, 1}; y1 = {1, 2, 1, 0, 1, 2, -1, 0, 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}] (* A194522 *) Table[y[n], {n, 1, 100}] (* A194523 *) 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-9) - a(n-10) for n > 10.
G.f.: x*(x^8 + x^7 - 3*x^6 + x^5 + x^4 - x^3 - x^2 + x + 1)/(x^10 - x^9 - x + 1). (End)
a(n) = n - 4*floor((n + 2)/9) - 2*floor((n + 5)/9) - 2*floor((n + 6)/9). - Ridouane Oudra, Dec 29 2020
Comments