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A194509
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Second coordinate of (2,3)-Lagrange pair for n.
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2
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1, 0, 1, 0, 1, 2, 1, 2, 1, 2, 3, 2, 3, 2, 3, 4, 3, 4, 3, 4, 5, 4, 5, 4, 5, 6, 5, 6, 5, 6, 7, 6, 7, 6, 7, 8, 7, 8, 7, 8, 9, 8, 9, 8, 9, 10, 9, 10, 9, 10, 11, 10, 11, 10, 11, 12, 11, 12, 11, 12, 13, 12, 13, 12, 13, 14, 13, 14, 13, 14, 15, 14, 15, 14, 15, 16, 15, 16, 15, 16, 17, 16
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OFFSET
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1,6
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COMMENTS
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See A194508.
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LINKS
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Table of n, a(n) for n=1..82.
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FORMULA
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From Chai Wah Wu, Jan 21 2020: (Start)
a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6.
G.f.: x*(x^4 - x^3 + x^2 - x + 1)/(x^6 - x^5 - x + 1). (End)
a(n) = n - 2*floor((2*n + 2)/5). - Ridouane Oudra, Dec 25 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).. -1..1..0..2..1..0..2..1..3..2...1...3...2
y(n)... 1..0..1..0..1..2..1..2..1..2...3...2...3
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MATHEMATICA
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c = 2; d = 3;
x1 = {-1, 1, 0, 2, 1}; y1 = {1, 0, 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}] (* A194508 *)
Table[y[n], {n, 1, 100}] (* A194509 *)
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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Cf. A194508.
Sequence in context: A265745 A092243 A257564 * A054716 A261641 A325622
Adjacent sequences: A194506 A194507 A194508 * A194510 A194511 A194512
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling, Aug 27 2011
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STATUS
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approved
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