A226782 If n == 0 (mod 2) then a(n) = 0, otherwise a(n) = 4^(-1) in Z/nZ*.

0, 0, 1, 0, 4, 0, 2, 0, 7, 0, 3, 0, 10, 0, 4, 0, 13, 0, 5, 0, 16, 0, 6, 0, 19, 0, 7, 0, 22, 0, 8, 0, 25, 0, 9, 0, 28, 0, 10, 0, 31, 0, 11, 0, 34, 0, 12, 0, 37, 0, 13, 0, 40, 0, 14, 0, 43, 0, 15, 0, 46, 0, 16, 0, 49, 0, 17

Offset

1,5

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 (0,0,0,2,0,0,0,-1).

Formula

From Colin Barker, Jun 20 2013: (Start)

G.f.: -x^3*(x^6 - 4*x^2 - 1) / ( (x-1)^2*(1+x)^2*(x^2+1)^2 ).

a(2n+1) = A225126(n+1). (End)

Maple

A226782 := proc(n)
    local x , a, m;
    a := 4 ;
    m := 2 ;
    if n mod m = 0 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[4, n], {n, 1, 122}]
(* Second program: *)
Table[If[EvenQ[n], 0, ModularInverse[4, n], 0], {n, 1, 100}] (* Jean-François Alcover, Mar 14 2023 *)

Prog

(PARI) a(n)=if(n%2, lift(Mod(1, n)/4), 0) \\ Charles R Greathouse IV, Jun 18 2013

Crossrefs

Cf. A092092, A226783, A226784, A226785, A226786, A226787.

Sequence in context: A067565 A243154 A307717 * A010635 A272198 A272203

Adjacent sequences: A226779 A226780 A226781 * A226783 A226784 A226785

Keyword

nonn,easy

Author

José María Grau Ribas, Jun 18 2013

Status

approved