cp's OEIS Frontend

A194526 First coordinate of (5,6)-Lagrange pair for n.

%I A194526 #15 Dec 30 2020 12:12:21
%S A194526 -1,-2,3,2,1,0,-1,-2,3,2,-1,0,-1,4,3,2,1,0,-1,4,3,0,1,0,5,4,3,2,1,0,5,
%T A194526 4,1,2,1,6,5,4,3,2,1,6,5,2,3,2,7,6,5,4,3,2,7,6,3,4,3,8,7,6,5,4,3,8,7,
%U A194526 4,5,4,9,8,7,6,5,4,9,8,5,6,5,10,9,8,7,6,5,10,9,6,7,6,11,10,9,8,7,6
%N A194526 First coordinate of (5,6)-Lagrange pair for n.
%C A194526 See A194508.
%H A194526 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,1,-1).
%F A194526 From _Chai Wah Wu_, Jan 21 2020: (Start)
%F A194526 a(n) = a(n-1) + a(n-11) - a(n-12) for n > 12.
%F A194526 G.f.: x*(2*x^11 - 3*x^10 - x^9 + 5*x^8 - x^7 - x^6 - x^5 - x^4 - x^3 + 5*x^2 - x - 1)/(x^12 - x^11 - x + 1). (End)
%F A194526 a(n) = 5*n - 2 - 2*floor(9*n/11) - 6*floor((9*n + 5)/11) + 2*floor((9*n + 10)/11). - _Ridouane Oudra_, Dec 30 2020
%e A194526 This table shows (x(n),y(n)) for 1<=n<=13:
%e A194526 n...... 1..2..3..4..5..6..7..8..9..10..11..12..13
%e A194526 x(n).. -1.-2..3..2..1..0.-1.-2..3..2..-1...0..-1
%e A194526 y(n)... 1..2.-2.-1..0..1..2..3.-1..0...2...2...3
%t A194526 c = 5; d = 6;
%t A194526 x1 = {-1, -2, 3, 2, 1, 0, -1, -2, 3, 2, -1}; y1 = {1, 2, -2, -1, 0, 1,
%t A194526    2, 3, -1, 0, 2};
%t A194526 x[n_] := If[n <= c + d, x1[[n]], x[n - c - d] + 1]
%t A194526 y[n_] := If[n <= c + d, y1[[n]], y[n - c - d] + 1]
%t A194526 Table[x[n], {n, 1, 100}]  (* A194526 *)
%t A194526 Table[y[n], {n, 1, 100}]  (* A194527 *)
%t A194526 r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]
%t A194526 TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 30}]]
%Y A194526 Cf. A194508, A194527.
%K A194526 sign
%O A194526 1,2
%A A194526 _Clark Kimberling_, Aug 28 2011