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

0,1

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

Table of n, a(n) for n=0..106.

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

Cf. A198517, A232991.

Sequence in context: A262805 A213728 A105367 * A285076 A338353 A267598

Adjacent sequences: A232987 A232988 A232989 * A232991 A232992 A232993

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 13 2013

Status

approved