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 A194528 First coordinate of (5,8)-Lagrange pair for n. 3

%I

%S -3,2,-1,4,1,-2,3,0,-3,2,-1,-4,1,-2,3,0,5,2,-1,4,1,-2,3,0,-3,2,-1,4,1,

%T 6,3,0,5,2,-1,4,1,-2,3,0,5,2,7,4,1,6,3,0,5,2,-1,4,1,6,3,8,5,2,7,4,1,6,

%U 3,0,5,2,7,4,9,6,3,8,5,2,7,4,1,6,3,8,5,10,7,4,9,6,3,8,5,2

%N First coordinate of (5,8)-Lagrange pair for n.

%C See A194508.

%F From _Chai Wah Wu_, Jan 24 2020: (Start)

%F a(n) = a(n-1) + a(n-13) - a(n-14) for n > 14.

%F G.f.: x*(5*x^12 - 3*x^11 - 3*x^10 + 5*x^9 - 3*x^8 - 3*x^7 + 5*x^6 - 3*x^5 - 3*x^4 + 5*x^3 - 3*x^2 + 5*x - 3)/(x^14 - x^13 - x + 1). (End)

%F a(n) = 5*n - 8*floor((4*n + 4)/13) - 8*floor((4*n + 9)/13). - _Ridouane Oudra_, Dec 29 2020

%e This table shows (x(n),y(n)) for 1<=n<=13:

%e n..... 1..2..3..4..5..6..7..8..9..10..11..12..13

%e x(n)..-3..2.-1..4..1.-2..3..0.-3..2..-1..-4...1

%e y(n).. 2.-1..1.-2..0..2.-1..1..3..0...2...4...1

%t c = 5; d = 8;

%t x1 = {-3, 2, -1, 4, 1, -2, 3, 0, -3, 2, -1, -4, 1};

%t y1 = {2, -1, 1, -2, 0, 2, -1, 1, 3, 0, 2, 4, 1};

%t x[n_] := If[n <= c + d, x1[[n]], x[n - c - d] + 1]

%t y[n_] := If[n <= c + d, y1[[n]], y[n - c - d] + 1]

%t Table[x[n], {n, 1, 100}] (* A194528 *)

%t Table[y[n], {n, 1, 100}] (* A194529 *)

%t r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]

%t TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 40}]]

%Y Cf. A194508, A194529.

%K sign

%O 1,1

%A _Clark Kimberling_, Aug 28 2011

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Last modified May 15 07:17 EDT 2021. Contains 343909 sequences. (Running on oeis4.)