OFFSET
1,1
COMMENTS
See A194508.
FORMULA
From Chai Wah Wu, Jan 24 2020: (Start)
a(n) = a(n-1) + a(n-13) - a(n-14) for n > 14.
G.f.: x*(5*x^12 - 3*x^11 - 3*x^10 + 5*x^9 - 3*x^8 - 3*x^7 + 5*x^6 - 3*x^5 - 3*x^4 + 5*x^3 - 3*x^2 + 5*x - 3)/(x^14 - x^13 - x + 1). (End)
a(n) = 5*n - 8*floor((4*n + 4)/13) - 8*floor((4*n + 9)/13). - Ridouane Oudra, Dec 29 2020
EXAMPLE
This table shows (x(n),y(n)) for 1<=n<=13:
n..... 1..2..3..4..5..6..7..8..9..10..11..12..13
x(n)..-3..2.-1..4..1.-2..3..0.-3..2..-1..-4...1
y(n).. 2.-1..1.-2..0..2.-1..1..3..0...2...4...1
MATHEMATICA
c = 5; d = 8;
x1 = {-3, 2, -1, 4, 1, -2, 3, 0, -3, 2, -1, -4, 1};
y1 = {2, -1, 1, -2, 0, 2, -1, 1, 3, 0, 2, 4, 1};
x[n_] := If[n <= c + d, x1[[n]], x[n - c - d] + 1]
y[n_] := If[n <= c + d, y1[[n]], y[n - c - d] + 1]
Table[x[n], {n, 1, 100}] (* A194528 *)
Table[y[n], {n, 1, 100}] (* A194529 *)
r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]
TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 40}]]
CROSSREFS
KEYWORD
sign
AUTHOR
Clark Kimberling, Aug 28 2011
STATUS
approved