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

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, 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, 0, 11, 0, 56, 0, 0

Offset: 1

Author

José María Grau Ribas, Jun 18 2013

Keywords

• nonn
• easy

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Bertrand Teguia Tabuguia and Wolfram Koepf, FPS In Action: An Easy Way To Find Explicit Formulas For Interlaced Hypergeometric Sequences, arXiv:2207.01031 [cs.SC], 2022.
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1).

Crossrefs

Cf. A092092, A226782, A226783, A226785, A226786, A226787.

Programs

Maple

A226784 := proc(n)
    local x,a,m ;
    a := 6 ;
    m := 6 ;
    if igcd(n,m) > 1 or n =1 then
        0;
    else
        msolve(x*a=1,n) ;
        op(%) ;
        op(2,%) ;
    end if;
end proc: # R. J. Mathar, Jun 28 2013

Mathematica

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}]
(* Second program: *)
Table[If[GCD[n, 6] != 1, 0, ModularInverse[6, n], 0], {n, 1, 100}] (* Jean-François Alcover, Mar 14 2023 *)

PARI

a(n)=if(gcd(n,6)>1,0,lift(Mod(1,n)/6)) \\ Charles R Greathouse IV, Jun 18 2013

Formula

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

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

a(n) = Sum_{k=1..n} k*(floor((6k-1)/n)-floor((6k-2)/n)), n>1. - Anthony Browne, Jun 19 2016

Extensions

Name corrected by David A. Corneth, Jun 20 2016