A232990 Period 5: repeat [1,0,0,1,0].

1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0

Offset: 0

Author

N. J. A. Sloane, Dec 13 2013

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A198517, A232991.

Programs

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

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 *)

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

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