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A194515 Second coordinate of (3,4)-Lagrange pair for n.

%I A194515 #15 Dec 29 2020 09:34:05
%S A194515 1,-1,0,1,2,0,1,2,0,1,2,3,1,2,3,1,2,3,4,2,3,4,2,3,4,5,3,4,5,3,4,5,6,4,
%T A194515 5,6,4,5,6,7,5,6,7,5,6,7,8,6,7,8,6,7,8,9,7,8,9,7,8,9,10,8,9,10,8,9,10,
%U A194515 11,9,10,11,9,10,11,12,10,11,12,10,11,12,13,11,12,13,11,12,13,14
%N A194515 Second coordinate of (3,4)-Lagrange pair for n.
%C A194515 See A194508.
%H A194515 <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 A194515 From _Chai Wah Wu_, Jan 21 2020: (Start)
%F A194515 a(n) = a(n-1) + a(n-7) - a(n-8) for n > 8.
%F A194515 G.f.: x*(x^6 - 2*x^5 + x^4 + x^3 + x^2 - 2*x + 1)/(x^8 - x^7 - x + 1). (End)
%F A194515 a(n) = n - 3*floor((2*n + 3)/7). - _Ridouane Oudra_, Dec 29 2020
%e A194515 This table shows (x(n),y(n)) for 1<=n<=13:
%e A194515 n...... 1..2..3..4..5..6..7..8..9..10..11..12..13
%e A194515 x(n)...-1..2..1..0.-1..2..1..0..3..2...1...0...3
%e A194515 y(n)... 1.-1..0..1..2..0..1..2..0..1...2...3...1
%t A194515 c = 3; d = 4;
%t A194515 x1 = {-1, 2, 1, 0, -1, 2, 1}; y1 = {1, -1, 0, 1, 2, 0, 1};
%t A194515 x[n_] := If[n <= c + d, x1[[n]], x[n - c - d] + 1]
%t A194515 y[n_] := If[n <= c + d, y1[[n]], y[n - c - d] + 1]
%t A194515 Table[x[n], {n, 1, 100}]  (* A194514 *)
%t A194515 Table[y[n], {n, 1, 100}]  (* A194515 *)
%t A194515 r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]
%t A194515 TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 30}]]
%Y A194515 Cf. A194508, A194514.
%K A194515 sign
%O A194515 1,5
%A A194515 _Clark Kimberling_, Aug 28 2011