A226786 -id:A226786 - cp's OEIS frontend

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

José María Grau Ribas, Jun 18 2013

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).

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

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

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 *)

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

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)

A226787 If n=0 (mod 3) then a(n)=0, otherwise a(n)=9^(-1) in Z/nZ*.

Original entry on oeis.org

0, 1, 0, 1, 4, 0, 4, 1, 0, 9, 5, 0, 3, 11, 0, 9, 2, 0, 17, 9, 0, 5, 18, 0, 14, 3, 0, 25, 13, 0, 7, 25, 0, 19, 4, 0, 33, 17, 0, 9, 32, 0, 24, 5, 0, 41, 21, 0, 11, 39, 0, 29, 6, 0, 49, 25, 0, 13, 46, 0, 34, 7, 0, 57, 29

Offset: 1

José María Grau Ribas, Jun 18 2013

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A092092, A226782-A226786.

Inv[a_, mod_] := Which[mod == 1,0, GCD[a, mod] > 1, 0, True, Last@Reduce[a*x == 1, x, Modulus -> mod]];Table[Inv[9, n], {n, 1, 122}]
(* Second program: *)
Table[If[Mod[n, 3] == 0, 0, ModularInverse[9, n], 0], {n, 1, 100}] (* Jean-François Alcover, Mar 14 2023 *)

a(n)=if(n%3,lift(Mod(1,n)/9),0) \\ Charles R Greathouse IV, Jun 18 2013

Empirical g.f.: -x^2*(x^17-x^14-3*x^12-x^11-3*x^9-9*x^8-x^6-4*x^5-4*x^3-x^2-1) / (x^18 -2*x^9 +1). - Colin Barker, Jun 20 2013

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

Original entry on oeis.org

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

José María Grau Ribas, Jun 18 2013

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).

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

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

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 *)

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

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

Name corrected by David A. Corneth, Jun 20 2016

cp's OEIS Frontend

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

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A226787 If n=0 (mod 3) then a(n)=0, otherwise a(n)=9^(-1) in Z/nZ*.

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

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