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%I A194510 #14 Dec 28 2020 14:42:43
%S A194510 3,1,-1,2,0,3,1,4,2,0,3,1,4,2,5,3,1,4,2,5,3,6,4,2,5,3,6,4,7,5,3,6,4,7,
%T A194510 5,8,6,4,7,5,8,6,9,7,5,8,6,9,7,10,8,6,9,7,10,8,11,9,7,10,8,11,9,12,10,
%U A194510 8,11,9,12,10,13,11,9,12,10,13,11,14,12,10,13,11,14,12,15,13,11,14
%N A194510 First coordinate of (2,5)-Lagrange pair for n.
%C A194510 See A194508.
%H A194510 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,-1).
%F A194510 From _Chai Wah Wu_, Jan 21 2020: (Start)
%F A194510 a(n) = a(n-1) + a(n-7) - a(n-8) for n > 8.
%F A194510 G.f.: x*(-2*x^6 + 3*x^5 - 2*x^4 + 3*x^3 - 2*x^2 - 2*x + 3)/(x^8 - x^7 - x + 1). (End)
%F A194510 a(n) = 3*n - 5*floor((4*n + 2)/7). - _Ridouane Oudra_, Dec 25 2020
%e A194510 This table shows (x(n),y(n)) for 1<=n<=13:
%e A194510 n...... 1..2..3..4..5..6..7..8..9..10..11..12..13
%e A194510 x(n)... 3..1.-1..2..0..3..1..4..2..0...3...1...4
%e A194510 y(n).. -1..0..1..0..1..0..1..0..1..2...1...2...1
%t A194510 c = 2; d = 5;
%t A194510 x1 = {3, 1, -1, 2, 0, 3, 1}; y1 = {-1, 0, 1, 0, 1, 0, 1};
%t A194510 x[n_] := If[n <= c + d, x1[[n]], x[n - c - d] + 1]
%t A194510 y[n_] := If[n <= c + d, y1[[n]], y[n - c - d] + 1]
%t A194510 Table[x[n], {n, 1, 100}] (* A194510 *)
%t A194510 Table[y[n], {n, 1, 100}] (* A194511 *)
%t A194510 r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]
%t A194510 TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 30}]]
%Y A194510 Cf. A194508, A194511.
%K A194510 sign
%O A194510 1,1
%A A194510 _Clark Kimberling_, Aug 27 2011

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