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A194521
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Second coordinate of (3,8)-Lagrange pair for n.
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3
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-1, 1, 0, -1, 1, 0, 3, 1, 0, -1, 1, 0, 2, 1, 0, 2, 1, 4, 2, 1, 0, 2, 1, 3, 2, 1, 3, 2, 5, 3, 2, 1, 3, 2, 4, 3, 2, 4, 3, 6, 4, 3, 2, 4, 3, 5, 4, 3, 5, 4, 7, 5, 4, 3, 5, 4, 6, 5, 4, 6, 5, 8, 6, 5, 4, 6, 5, 7, 6, 5, 7, 6, 9, 7, 6, 5, 7, 6, 8, 7, 6, 8, 7, 10, 8, 7, 6, 8, 7, 9, 8, 7, 9, 8, 11, 9
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OFFSET
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1,7
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COMMENTS
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,1,-1).
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FORMULA
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a(n) = a(n-1) + a(n-11) - a(n-12) for n > 12.
G.f.: x*(2*x^10 - x^9 - x^8 - 2*x^7 + 3*x^6 - x^5 + 2*x^4 - x^3 - x^2 + 2*x - 1)/(x^12 - x^11 - x + 1). (End)
a(n) = 2*n - 4*floor((7*n + 5)/11) + 4*floor((7*n + 6)/11) - 3*floor((7*n + 7)/11). - Ridouane Oudra, Dec 29 2020
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EXAMPLE
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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
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MATHEMATICA
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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}]]
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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