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A226784 If gcd(n,6) != 1 then a(n)=0, otherwise a(n)=6^(-1) in Z/nZ*.

%I A226784 #37 Mar 14 2023 11:45:22
%S A226784 0,0,0,0,1,0,6,0,0,0,2,0,11,0,0,0,3,0,16,0,0,0,4,0,21,0,0,0,5,0,26,0,
%T A226784 0,0,6,0,31,0,0,0,7,0,36,0,0,0,8,0,41,0,0,0,9,0,46,0,0,0,10,0,51,0,0,
%U A226784 0,11,0,56,0,0
%N A226784 If gcd(n,6) != 1 then a(n)=0, otherwise a(n)=6^(-1) in Z/nZ*.
%H A226784 Charles R Greathouse IV, <a href="/A226784/b226784.txt">Table of n, a(n) for n = 1..10000</a>
%H A226784 Bertrand Teguia Tabuguia and Wolfram Koepf, <a href="https://arxiv.org/abs/2207.01031">FPS In Action: An Easy Way To Find Explicit Formulas For Interlaced Hypergeometric Sequences</a>, arXiv:2207.01031 [cs.SC], 2022.
%H A226784 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1).
%F A226784 G.f.: -x^5*(x^8-6*x^2-1) / (x^12-2*x^6+1). a(n) = 2*a(n-6)-a(n-12). - _Colin Barker_, Jun 20 2013
%F A226784 a(6n+1) = A016861(n), n>0. a(6n+2) = a(6n+3) = a(6n+4) = 0. a(6n+5)=n+1. - _R. J. Mathar_, Jun 28 2013
%F A226784 a(n) = Sum_{k=1..n} k*(floor((6k-1)/n)-floor((6k-2)/n)), n>1. - _Anthony Browne_, Jun 19 2016
%p A226784 A226784 := proc(n)
%p A226784     local x,a,m ;
%p A226784     a := 6 ;
%p A226784     m := 6 ;
%p A226784     if igcd(n,m) > 1 or n =1 then
%p A226784         0;
%p A226784     else
%p A226784         msolve(x*a=1,n) ;
%p A226784         op(%) ;
%p A226784         op(2,%) ;
%p A226784     end if;
%p A226784 end proc: # _R. J. Mathar_, Jun 28 2013
%t A226784 Inv[a_, mod_] := Which[mod == 1,0, GCD[a, mod] > 1, 0, True, Last@Reduce[a*x == 1, x, Modulus -> mod]];Table[Inv[6, n], {n, 1, 122}]
%t A226784 (* Second program: *)
%t A226784 Table[If[GCD[n, 6] != 1, 0, ModularInverse[6, n], 0], {n, 1, 100}] (* _Jean-François Alcover_, Mar 14 2023 *)
%o A226784 (PARI) a(n)=if(gcd(n,6)>1,0,lift(Mod(1,n)/6)) \\ _Charles R Greathouse IV_, Jun 18 2013
%Y A226784 Cf. A092092, A226782, A226783, A226785, A226786, A226787.
%K A226784 nonn,easy
%O A226784 1,7
%A A226784 _José María Grau Ribas_, Jun 18 2013
%E A226784 Name corrected by _David A. Corneth_, Jun 20 2016