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%I #25 Jan 06 2020 18:48:01
%S 0,1,0,25,0,9,0,17,0,17,0,9,0,25,0,1,0,1,0,25,0,9,0,17,0,17,0,9,0,25,
%T 0,1,0,1,0,25,0,9,0,17,0,17,0,9,0,25,0,1,0,1,0,25,0,9,0,17,0,17,0,9,0,
%U 25,0,1,0,1,0,25,0,9,0,17,0,17,0,9,0,25,0,1,0,1,0,25,0,9,0,17,0,17,0,9,0
%N a(n) = n^6 mod 32.
%C Equivalently: n^(8*m+6) (mod 32). - _G. C. Greubel_, Jun 17 2016
%H Vincenzo Librandi, <a href="/A167624/b167624.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n+16) = a(n). - _G. C. Greubel_, Jun 17 2016
%F From _Chai Wah Wu_, Jan 06 2020: (Start)
%F a(n) = a(n-2) - a(n-4) + a(n-6) - a(n-8) + a(n-10) - a(n-12) + a(n-14) for n > 13.
%F G.f.: (-x^13 - 24*x^11 + 15*x^9 - 32*x^7 + 15*x^5 - 24*x^3 - x)/((x - 1)*(x + 1)*(x^4 + 1)*(x^8 + 1)). (End)
%t PowerMod[Range[0,100],6,32] (* _Harvey P. Dale_, Apr 03 2015 *)
%o (Sage) [power_mod(n,6,32) for n in range(0, 100)] #
%o (PARI) a(n)=n^6%32 \\ _Charles R Greathouse IV_, Apr 06 2016
%K nonn,easy
%O 0,4
%A _Zerinvary Lajos_, Nov 07 2009
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