A272648 a(n) = A002119(n) mod 7.

1, 1, 0, 1, 0, 1, 1, 6, 6, 0, 6, 0, 6, 6, 1, 1, 0, 1, 0, 1, 1, 6, 6, 0, 6, 0, 6, 6, 1, 1, 0, 1, 0, 1, 1, 6, 6, 0, 6, 0, 6, 6, 1, 1, 0, 1, 0, 1, 1, 6, 6, 0, 6, 0, 6, 6, 1, 1, 0, 1, 0, 1, 1, 6, 6, 0, 6, 0, 6, 6, 1, 1, 0, 1, 0, 1, 1, 6, 6, 0, 6

Offset

0,8

Comments

Periodic with period 14.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

D. H. Lehmer, Arithmetical periodicities of Bessel functions, Annals of Mathematics, 33 (1932): 143-150. The sequence is on page 149.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Formula

G.f.: (1+x+x^3+x^5+x^6)*(1+6*x^7) / ((1-x)*(1+x)*(1-x+x^2-x^3+x^4-x^5+x^6)*(1+x+x^2+x^3+x^4+x^5+x^6)). - Colin Barker, May 10 2016

a(n) = (-m^6+18*m^5-122*m^4+384*m^3-549*m^2+270*m+24)*(7-5*(-1)^floor(n/7))/48, where m = (n mod 7). - Luce ETIENNE, Sep 21 2018

Maple

f:=proc(n) option remember; if n = 0 then 1 elif n=1 then 1 else f(n-2)+(4*n-2)*f(n-1); fi; end;
[seq(f(n) mod 7, n=0..120)];

Mathematica

PadRight[{}, 120, {1, 1, 0, 1, 0, 1, 1, 6, 6, 0, 6, 0, 6, 6}] (* Harvey P. Dale, Jun 07 2016 *)

Prog

(PARI) Vec((1+x+x^3+x^5+x^6)*(1+6*x^7)/((1-x)*(1+x)*(1-x+x^2-x^3+x^4-x^5+x^6)*(1+x+x^2+x^3+x^4+x^5+x^6)) + O(x^50)) \\ Colin Barker, May 10 2016
(GAP) b:=[1, -1];; for n in [3..95] do b[n]:=-2*(2*n-3)*b[n-1]+b[n-2]; od; a:=List(b, AbsInt) mod 7; # Muniru A Asiru, Sep 20 2018

Crossrefs

Cf. A001517, A002119, A272647.

Cf. A010876.

Sequence in context: A197013 A329092 A081825 * A212708 A028969 A029681

Adjacent sequences: A272645 A272646 A272647 * A272649 A272650 A272651

Keyword

nonn,easy

Author

N. J. A. Sloane, May 09 2016

Status

approved