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%I #17 Aug 17 2019 14:50:06
%S 1,0,7,2,5,6,5,2,7,0,1,0,7,2,5,6,5,2,7,0,1,0,7,2,5,6,5,2,7,0,1,0,7,2,
%T 5,6,5,2,7,0,1,0,7,2,5,6,5,2,7,0,1,0,7,2,5,6,5,2,7,0,1,0,7,2,5,6,5,2,
%U 7,0,1,0,7,2,5,6,5,2,7,0,1,0,7,2,5,6
%N Units' digits of the nonzero decagonal numbers.
%C This is a periodic sequence with period 10 and cycle 1,0,7,2,5,6,5,2,7,0.
%F a(n) = a(n-10).
%F a(n) = 35 -a(n-1) -a(n-2) -a(n-3) -a(n-4) -a(n-5) -a(n-6) -a(n-7) -a(n-8) -a(n-9).
%F a(n) = mod(n(4n-3),10).
%F G.f.: x*(1 +7*x^2 +2*x^3 +5*x^4 +6*x^5 +5*x^6 +2*x^7 +7*x^8)/((1-x)*(1+x)*(1 +x +x^2 +x^3 +x^4)*(1 -x +x^2 -x^3 +x^4)).
%F a(n) = -n^2 + 2*n (mod 10). - _Arkadiusz Wesolowski_, Jul 03 2012
%F a(n) = A010879(A001107(n)). - _Michel Marcus_, Aug 10 2015
%e The seventh nonzero decagonal number is A001107(7)=175, which has units' digit 5. Hence a(7)=5.
%t Table[Mod[n (4 n - 3), 10], {n, 86}]
%t PadRight[{},120,{1,0,7,2,5,6,5,2,7,0}] (* _Harvey P. Dale_, Aug 17 2019 *)
%Y Cf. A001107, A010879.
%K nonn,easy,base
%O 1,3
%A _Ant King_, Sep 07 2011