A194511 - OEIS

%I #16 Feb 04 2022 09:26:58

%S -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 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 10,9,10,9,10,11,10,11,10,11,10,11,12,11,12,11,12,11,12,13,12,13

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

%C See A194508.

%H <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 From _Chai Wah Wu_, Jan 21 2020: (Start)

%F a(n) = a(n-1) + a(n-7) - a(n-8) for n > 8.

%F G.f.: x*(x^6 - x^5 + x^4 - x^3 + x^2 + x - 1)/(x^8 - x^7 - x + 1). (End)

%F a(n) = n - 2*floor((3*n + 4)/7). - _Ridouane Oudra_, Dec 25 2020

%F 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 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..1.-1..2..0..3..1..4..2..0...3...1...4

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

%t c = 2; d = 5;

%t x1 = {3, 1, -1, 2, 0, 3, 1}; y1 = {-1, 0, 1, 0, 1, 0, 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}] (* A194510 *)

%t Table[y[n], {n, 1, 100}] (* A194511 *)

%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, 30}]]

%Y Cf. A194508, A194510.

%K sign,easy

%O 1,10

%A _Clark Kimberling_, Aug 27 2011