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A194525
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Second coordinate of (4,7)-Lagrange pair for n.
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3
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-1, -2, 1, 0, -1, 2, 1, 0, -1, 2, 1, 0, -1, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 4, 3, 2, 1, 4, 3, 2, 1, 4, 3, 2, 5, 4, 3, 2, 5, 4, 3, 2, 5, 4, 3, 6, 5, 4, 3, 6, 5, 4, 3, 6, 5, 4, 7, 6, 5, 4, 7, 6, 5, 4, 7, 6, 5, 8, 7, 6, 5, 8, 7, 6, 5, 8, 7, 6, 9, 8, 7, 6, 9, 8, 7, 6, 9, 8, 7
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OFFSET
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1,2
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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..93.
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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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^10 + 3*x^9 - x^8 - x^7 - x^6 + 3*x^5 - x^4 - x^3 + 3*x^2 - x - 1)/(x^12 - x^11 - x + 1). (End)
a(n) = 3*n - 4*floor((8*n + 6)/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).. 2..4.-1..1..3.-2..0..2..4.-1...1...3...5
y(n). -1.-2..1..0.-1..2..1..0.-1..2...1...0..-1
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MATHEMATICA
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c = 4; d = 7;
x1 = {2, 4, -1, 1, 3, -2, 0, 2, 4, -1, 1};
y1 = {-1, -2, 1, 0, -1, 2, 1, 0, -1, 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}] (* A194524 *)
Table[y[n], {n, 1, 100}] (* A194525 *)
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, A194524.
Sequence in context: A284171 A286320 A330888 * A330466 A282938 A065368
Adjacent sequences: A194522 A194523 A194524 * A194526 A194527 A194528
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KEYWORD
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sign
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AUTHOR
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Clark Kimberling, Aug 28 2011
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STATUS
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approved
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