OFFSET
0,1
COMMENTS
Sequences of period k composed of (k-p) zeros followed by p ones have a closed formula of floor((n mod k)/(k-p)) for p >= floor(k/2). - Gary Detlefs, May 18 2011
a(n+3) is the determinant of an n X n pentadiagonal symmetric Toeplitz matrix with a=b=c=1. - R. J. Mathar, Jan 31 2023
LINKS
J. Borowska and L. Lacinska, Recurrence form of determinant of a heptadiagonal symmetric Toeplitz matrix, J. Appl. Math. Comp. Mech. 13 (2014) 19-16, remark 1 for determinant of Toeplitz matrices a=b=c=1.
R. Gold, Characteristic linear sequences and their coset functions, J. SIAM Applied. Math., 14 (1966), 980-985.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1).
FORMULA
a(n) = floor((n mod 5)/3). - Gary Detlefs, May 18 2011
a(n+4) = abs(a(n) - a(n+1) + a(n+2) - a(n+3)). - Benjamin Knight, May 06 2018
a(n) = (2/5) * (1 + cos(4*(n-4)*Pi/5) + cos(2*(n-3)*Pi/5) + cos(4*(n-3)*Pi/5) + cos(2*(n+1)*Pi/5)). - Wesley Ivan Hurt, Sep 26 2018
G.f.: -x^3*(1+x) / ( (x-1)*(1+x+x^2+x^3+x^4) ). - R. J. Mathar, Aug 11 2021
a(n) = floor(2*n/5) - 2*floor(n/5). - Ridouane Oudra, Apr 01 2023
MAPLE
seq(floor(2*n/5) - 2*floor(n/5), n=0..100); # Ridouane Oudra, Apr 01 2023
MATHEMATICA
PadRight[{}, 120, {0, 0, 0, 1, 1}] (* Harvey P. Dale, Dec 16 2015 *)
PROG
(PARI) a(n)=(n%5)\3 \\ Charles R Greathouse IV, Jan 16 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved