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%I #28 Sep 21 2018 02:54:50
%S 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,
%T 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,
%U 6,6,1,1,0,1,0,1,1,6,6,0,6
%N a(n) = A002119(n) mod 7.
%C Periodic with period 14.
%H Colin Barker, <a href="/A272648/b272648.txt">Table of n, a(n) for n = 0..1000</a>
%H D. H. Lehmer, <a href="http://www.jstor.org/stable/1968107">Arithmetical periodicities of Bessel functions</a>, Annals of Mathematics, 33 (1932): 143-150. The sequence is on page 149.
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,1).
%F 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
%F 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
%p 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;
%p [seq(f(n) mod 7, n=0..120)];
%t PadRight[{},120,{1,1,0,1,0,1,1,6,6,0,6,0,6,6}] (* _Harvey P. Dale_, Jun 07 2016 *)
%o (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
%o (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
%Y Cf. A001517, A002119, A272647.
%Y Cf. A010876.
%K nonn,easy
%O 0,8
%A _N. J. A. Sloane_, May 09 2016
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