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A226783
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If n=0 (mod 5) then a(n)=0, otherwise a(n)=5^(-1) in Z/nZ*.
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3
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0, 1, 2, 1, 0, 5, 3, 5, 2, 0, 9, 5, 8, 3, 0, 13, 7, 11, 4, 0, 17, 9, 14, 5, 0, 21, 11, 17, 6, 0, 25, 13, 20, 7, 0, 29, 15, 23, 8, 0, 33, 17, 26, 9, 0, 37, 19, 29, 10, 0, 41, 21, 32, 11, 0, 45, 23, 35, 12, 0, 49, 25, 38
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OFFSET
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1,3
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,2,0,0,0,0,-1).
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FORMULA
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G.f.: -x^2*(x^9-x^6-x^5-5*x^4-x^2-2*x-1) / ( (x-1)^2*(x^4+x^3+x^2+x+1)^2 ). - Colin Barker, Jun 20 2013
a(n) = Sum_{k=1..n} k*(floor((5k-1)/n)-floor((5k-2)/n)), n>1. - Anthony Browne, Jun 19 2016
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MAPLE
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local x ;
a := 5 ;
m := 5 ;
if n mod m = 0 or n = 1 then
0;
else
msolve(x*a=1, n) ;
op(%) ;
op(2, %) ;
end if;
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MATHEMATICA
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Inv[a_, mod_] := Which[mod == 1, 0, GCD[a, mod] > 1, 0, True, Last@Reduce[a*x == 1, x, Modulus -> mod]]; Table[Inv[5, n], {n, 1, 122}]
CoefficientList[Series[-x^2(x^9-x^6-x^5-5x^4-x^2-2x-1)/((x-1)^2 (x^4+ x^3+ x^2+ x+ 1)^2), {x, 0, 120}], x] (* Harvey P. Dale, Oct 08 2016 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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