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A272647 a(n) = A001517(n) mod 7.

%I A272647 #25 Jul 17 2020 18:11:14
%S A272647 1,3,5,4,5,3,1,1,3,5,4,5,3,1,1,3,5,4,5,3,1,1,3,5,4,5,3,1,1,3,5,4,5,3,
%T A272647 1,1,3,5,4,5,3,1,1,3,5,4,5,3,1,1,3,5,4,5,3,1,1,3,5,4,5,3,1,1,3,5,4,5,
%U A272647 3,1,1,3,5,4,5,3,1,1,3,5,4,5,3,1,1,3,5,4,5,3,1
%N A272647 a(n) = A001517(n) mod 7.
%C A272647 Periodic with period length 7.
%H A272647 Colin Barker, <a href="/A272647/b272647.txt">Table of n, a(n) for n = 0..1000</a>
%H A272647 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 A272647 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,1).
%F A272647 G.f.: (1 + 3*x + 5*x^2 + 4*x^3 + 5*x^4 + 3*x^5 + x^6) / ((1 - x)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)). - _Colin Barker_, May 10 2016
%F A272647 a(n) = (3*m^6 - 54*m^5 + 365*m^4 - 1140*m^3 + 1582*m^2 - 636*m + 60)/60, where m = n mod 7. - _Luce ETIENNE_, Oct 18 2018
%p A272647 f:=proc(n) option remember; if n = 0 then 1 elif n=1 then 3 else f(n-2)+(4*n-2)*f(n-1); fi; end;
%p A272647 [seq(f(n) mod 7, n=0..120)];
%t A272647 PadRight[{},120,{1,3,5,4,5,3,1}] (* _Harvey P. Dale_, Jul 17 2020 *)
%o A272647 (PARI) Vec((1+3*x+5*x^2+4*x^3+5*x^4+3*x^5+x^6)/((1-x)*(1+x+x^2+x^3+x^4+x^5+x^6)) + O(x^50)) \\ _Colin Barker_, May 10 2016
%Y A272647 Cf. A001517, A002119, A272648.
%Y A272647 Cf. A010876.
%K A272647 nonn,easy
%O A272647 0,2
%A A272647 _N. J. A. Sloane_, May 09 2016