OFFSET
0,1
COMMENTS
Used by R. J. Baxter in studying the Rogers-Ramanujan identities.
REFERENCES
Andrews, George E., q-series: their development and application in analysis, number theory, combinatorics, physics, and computer algebra. CBMS Regional Conference Series in Mathematics, 66. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1986. xii+130 pp. ISBN: 0-8218-0716-1 MR0858826 (88b:11063). See p. 105.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1).
FORMULA
a(n) = A198517(n+2).
a(n) = 2 + floor(n/5) - ceiling(n/5) + floor((n - 3)/5) - ceiling((n - 3)/5). - Wesley Ivan Hurt, Mar 13 2014
G.f.: -(x + 1)*(x^2 - x + 1)/((x - 1)*(x^4 + x^3 + x^2 + x + 1)). - Colin Barker, Mar 14 2014
a(n) = floor(((2*n - 2) mod 5)/3). - Wesley Ivan Hurt, Apr 30 2015
a(n) = (2/5)*(1 + cos(2*(n-3)*Pi/5) + cos(4*(n-3)*Pi/5) + cos(2*n*Pi/5) + cos(4*n*Pi/5)). - Wesley Ivan Hurt, Sep 26 2018
MAPLE
A232990:=n->2 + floor(n/5) - ceil(n/5) + floor((n-3)/5) - ceil((n-3)/5); # Wesley Ivan Hurt, Mar 13 2014
MATHEMATICA
Table[2 + Floor[n/5] - Ceiling[n/5] + Floor[(n - 3)/5] - Ceiling[(n - 3)/5], {n, 0, 100}] (* Wesley Ivan Hurt, Mar 13 2014 *)
PROG
(PARI) Vec(-(x+1)*(x^2-x+1)/((x-1)*(x^4+x^3+x^2+x+1)) + O(x^100)) \\ Colin Barker, Mar 14 2014
(PARI) a(n)=((2*n-2)%5)\3 \\ Charles R Greathouse IV, Apr 30 2015
(Magma) /* By definition: */ &cat [[1, 0, 0, 1, 0]: n in [0..20]]; // Bruno Berselli, Feb 18 2015
(Magma) [(((n+1) mod 5) mod 3) mod 2: n in [0..100]]; // Vincenzo Librandi, Feb 18 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 13 2013
STATUS
approved