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A194511 Second coordinate of (2,5)-Lagrange pair for n.

%I A194511 #16 Feb 04 2022 09:26:58
%S A194511 -1,0,1,0,1,0,1,0,1,2,1,2,1,2,1,2,3,2,3,2,3,2,3,4,3,4,3,4,3,4,5,4,5,4,
%T A194511 5,4,5,6,5,6,5,6,5,6,7,6,7,6,7,6,7,8,7,8,7,8,7,8,9,8,9,8,9,8,9,10,9,
%U A194511 10,9,10,9,10,11,10,11,10,11,10,11,12,11,12,11,12,11,12,13,12,13
%N A194511 Second coordinate of (2,5)-Lagrange pair for n.
%C A194511 See A194508.
%H A194511 <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 A194511 From _Chai Wah Wu_, Jan 21 2020: (Start)
%F A194511 a(n) = a(n-1) + a(n-7) - a(n-8) for n > 8.
%F A194511 G.f.: x*(x^6 - x^5 + x^4 - x^3 + x^2 + x - 1)/(x^8 - x^7 - x + 1). (End)
%F A194511 a(n) = n - 2*floor((3*n + 4)/7). - _Ridouane Oudra_, Dec 25 2020
%F A194511 G.f.: x*(1-x^2+x^3)*(x^3+x-1)/((1-x)^2*(1+x+x^2+x^3+x^4+x^5+x^6)). - _R. J. Mathar_, Feb 04 2022
%e A194511 This table shows (x(n),y(n)) for 1<=n<=13:
%e A194511 n...... 1..2..3..4..5..6..7..8..9..10..11..12..13
%e A194511 x(n)... 3..1.-1..2..0..3..1..4..2..0...3...1...4
%e A194511 y(n).. -1..0..1..0..1..0..1..0..1..2...1...2...1
%t A194511 c = 2; d = 5;
%t A194511 x1 = {3, 1, -1, 2, 0, 3, 1}; y1 = {-1, 0, 1, 0, 1, 0, 1};
%t A194511 x[n_] := If[n <= c + d, x1[[n]], x[n - c - d] + 1]
%t A194511 y[n_] := If[n <= c + d, y1[[n]], y[n - c - d] + 1]
%t A194511 Table[x[n], {n, 1, 100}] (* A194510 *)
%t A194511 Table[y[n], {n, 1, 100}] (* A194511 *)
%t A194511 r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]
%t A194511 TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 30}]]
%Y A194511 Cf. A194508, A194510.
%K A194511 sign,easy
%O A194511 1,10
%A A194511 _Clark Kimberling_, Aug 27 2011